1. Relational topology [2018]
- Book
- xiv, 191 pages : illustrations (some color) ; 24 cm.
- 1.Introduction.- 2. Prerequisites.- 3. Products of Relations.- 4. Meet and Join as Relations.- 5. Applying Relations in Topology.- 6. Construction of Topologies.- 7. Closures and their Aumann Contacts.- 8. Proximity and Nearness.- 9. Frames.- 10. Simplicial Complexes.
- (source: Nielsen Book Data)9783319744506 20180723
(source: Nielsen Book Data)9783319744506 20180723
- 1.Introduction.- 2. Prerequisites.- 3. Products of Relations.- 4. Meet and Join as Relations.- 5. Applying Relations in Topology.- 6. Construction of Topologies.- 7. Closures and their Aumann Contacts.- 8. Proximity and Nearness.- 9. Frames.- 10. Simplicial Complexes.
- (source: Nielsen Book Data)9783319744506 20180723
(source: Nielsen Book Data)9783319744506 20180723
Science Library (Li and Ma)
Science Library (Li and Ma) | Status |
---|---|
Serials | |
Shelved by Series title V.2208 | Unknown |
- Book
- x, 399 pages : illustrations ; 26 cm
- PrefaceI Euclidean Topology1. Introduction to Topology1.1 Deformations1.2 Topological Spaces2. Metric Topology in Euclidean Space2.1 Distance2.2 Continuity and Homeomorphism2.3 Compactness and Limits2.4 Connectedness2.5 Metric Spaces in General3. Vector Fields in the Plane3.1 Trajectories and Phase Portraits3.2 Index of a Critical Point3.3 *Nullclines and Trapping RegionsII Abstract Topology with Applications4. Abstract Point-Set Topology4.1 The Definition of a Topology4.2 Continuity and Limits4.3 Subspace Topology and Quotient Topology4.4 Compactness and Connectedness4.5 Product and Function Spaces4.6 *The Infinitude of the Primes5. Surfaces5.1 Surfaces and Surfaces-with-Boundary5.2 Plane Models and Words5.3 Orientability5.4 Euler Characteristic6. Applications in Graphs and Knots6.1 Graphs and Embeddings6.2 Graphs, Maps, and Coloring Problems6.3 Knots and Links6.4 Knot ClassificationIII Basic Algebraic Topology7. The Fundamental Group7.1 Algebra of Loops7.2 Fundamental Group as Topological Invariant7.3 Covering Spaces and the Circle7.4 Compact Surfaces and Knot Complements7.5 *Higher Homotopy Groups8. Introduction to Homology8.1 Rational Homology8.2 Integral HomologyAppendixesA. Review of Set Theory and FunctionsA.1 Sets and Operations on SetsA.2 Relations and FunctionsB. Group Theory and Linear AlgebraB.1 GroupsB.2 Linear AlgebraC. Selected SolutionsD. NotationsBibliographyIndex.
- (source: Nielsen Book Data)9781421424071 20180226
(source: Nielsen Book Data)9781421424071 20180226
- PrefaceI Euclidean Topology1. Introduction to Topology1.1 Deformations1.2 Topological Spaces2. Metric Topology in Euclidean Space2.1 Distance2.2 Continuity and Homeomorphism2.3 Compactness and Limits2.4 Connectedness2.5 Metric Spaces in General3. Vector Fields in the Plane3.1 Trajectories and Phase Portraits3.2 Index of a Critical Point3.3 *Nullclines and Trapping RegionsII Abstract Topology with Applications4. Abstract Point-Set Topology4.1 The Definition of a Topology4.2 Continuity and Limits4.3 Subspace Topology and Quotient Topology4.4 Compactness and Connectedness4.5 Product and Function Spaces4.6 *The Infinitude of the Primes5. Surfaces5.1 Surfaces and Surfaces-with-Boundary5.2 Plane Models and Words5.3 Orientability5.4 Euler Characteristic6. Applications in Graphs and Knots6.1 Graphs and Embeddings6.2 Graphs, Maps, and Coloring Problems6.3 Knots and Links6.4 Knot ClassificationIII Basic Algebraic Topology7. The Fundamental Group7.1 Algebra of Loops7.2 Fundamental Group as Topological Invariant7.3 Covering Spaces and the Circle7.4 Compact Surfaces and Knot Complements7.5 *Higher Homotopy Groups8. Introduction to Homology8.1 Rational Homology8.2 Integral HomologyAppendixesA. Review of Set Theory and FunctionsA.1 Sets and Operations on SetsA.2 Relations and FunctionsB. Group Theory and Linear AlgebraB.1 GroupsB.2 Linear AlgebraC. Selected SolutionsD. NotationsBibliographyIndex.
- (source: Nielsen Book Data)9781421424071 20180226
(source: Nielsen Book Data)9781421424071 20180226
Science Library (Li and Ma)
Science Library (Li and Ma) | Status |
---|---|
Stacks | |
QA611 .A86 2018 | Unknown |
- Book
- 1 online resource () : color illustrations.
- 1 Introduction 1.1 Scope of the Thesis 1.2 Outline of the Thesis 1.3 Quantum Hall States 1.4 Topological Insulators 1.5 Weyl and Dirac Semimetals 1.6 -(BEDT-TTF)2I3 1.7 Topological Mott Insulators 1.8 Topological Crystalline Insulators 1.9 Classification of Topological States of Matter 2 Interacting Dirac Fermions in (3+1) Dimensions 2.1 Model 2.2 Renormalization Group Analysis 2.3 Density of States 2.4 Electromagnetic Properties 2.5 Spectral Function 2.6 Electric Conductivity 2.7 Energy Gap 2.8 Discussions and Summary 3 Tilted Dirac Cones in Two Dimensions 3.1 Model 3.2 Perturbative Renormalization Group Analysis 3.3 Spin Susceptibility 3.4 Discussions and Summary 4 Generalized Hund's Rule for Two-Atom Systems 4.1 Model 4.2 Results 4.3 Perturbative Calculation 4.4 Entanglement Entropy 4.5 Symmetry 4.6 Discussions and Summary 5 Interacting Topological Crystalline Insulators 5.1 Classification in Two Dimensions 5.2 Interacting TCIs in Three Dimensions 5.3 Discussions and Summary 6 Conclusions and Prospects.
- (source: Nielsen Book Data)9789811037429 20180730
(source: Nielsen Book Data)9789811037429 20180730
- 1 Introduction 1.1 Scope of the Thesis 1.2 Outline of the Thesis 1.3 Quantum Hall States 1.4 Topological Insulators 1.5 Weyl and Dirac Semimetals 1.6 -(BEDT-TTF)2I3 1.7 Topological Mott Insulators 1.8 Topological Crystalline Insulators 1.9 Classification of Topological States of Matter 2 Interacting Dirac Fermions in (3+1) Dimensions 2.1 Model 2.2 Renormalization Group Analysis 2.3 Density of States 2.4 Electromagnetic Properties 2.5 Spectral Function 2.6 Electric Conductivity 2.7 Energy Gap 2.8 Discussions and Summary 3 Tilted Dirac Cones in Two Dimensions 3.1 Model 3.2 Perturbative Renormalization Group Analysis 3.3 Spin Susceptibility 3.4 Discussions and Summary 4 Generalized Hund's Rule for Two-Atom Systems 4.1 Model 4.2 Results 4.3 Perturbative Calculation 4.4 Entanglement Entropy 4.5 Symmetry 4.6 Discussions and Summary 5 Interacting Topological Crystalline Insulators 5.1 Classification in Two Dimensions 5.2 Interacting TCIs in Three Dimensions 5.3 Discussions and Summary 6 Conclusions and Prospects.
- (source: Nielsen Book Data)9789811037429 20180730
(source: Nielsen Book Data)9789811037429 20180730
EBSCOhost Access limited to 1 user
- EBSCOhost Access limited to 1 user
- Google Books (Full view)
4. Recent progress in general topology III [2014]
- Book
- 1 online resource (880 pages) : illustrations
- Topological Homogeneity.- Some Recent Progress Concerning Topology of Fractals.- A biased view of topology as a tool in functional analysis.- Large scale versus small scale.- Descriptive aspects of Rosenthal compacta.- Minimality conditions in topological groups.- Set-Theoretic update on Topology.- Topics in Dimension Theory.- Representations of dynamical systems on Banach spaces.- Generalized metrizable spaces.- Permanence in Coarse Geometry.- Selections and Hyperspaces.- Continuum Theory.- Almost disjoint families and topology.- Some Topics in Geometric Topology II.- Topological aspects of dynamics of pairs, tuples and sets.- Continuous selections of multivalued mappings.- The combinatorics of open covers.- Covering properties.- Paratopological and semitopological groups vs topological groups.
- (source: Nielsen Book Data)9789462390232 20160614
(source: Nielsen Book Data)9789462390232 20160614
- Topological Homogeneity.- Some Recent Progress Concerning Topology of Fractals.- A biased view of topology as a tool in functional analysis.- Large scale versus small scale.- Descriptive aspects of Rosenthal compacta.- Minimality conditions in topological groups.- Set-Theoretic update on Topology.- Topics in Dimension Theory.- Representations of dynamical systems on Banach spaces.- Generalized metrizable spaces.- Permanence in Coarse Geometry.- Selections and Hyperspaces.- Continuum Theory.- Almost disjoint families and topology.- Some Topics in Geometric Topology II.- Topological aspects of dynamics of pairs, tuples and sets.- Continuous selections of multivalued mappings.- The combinatorics of open covers.- Covering properties.- Paratopological and semitopological groups vs topological groups.
- (source: Nielsen Book Data)9789462390232 20160614
(source: Nielsen Book Data)9789462390232 20160614
- Book
- xi, 349 p. : ill.
7. A guide to topology [2009]
- Book
- xii, 107 p. : ill. ; 24 cm.
- Preface-- Part I. Fundamentals: 1.1. What is topology?-- 1.2. First definitions-- 1.3 Mappings-- 1.4. The separation axioms-- 1.5. Compactness-- 1.6. Homeomorphisms-- 1.7. Connectedness-- 1.8. Path-connectedness-- 1.9. Continua-- 1.10. Totally disconnected spaces-- 1.11. The Cantor set-- 1.12. Metric spaces-- 1.13. Metrizability-- 1.14. Baire's theorem-- 1.15. Lebesgue's lemma and Lebesgue numbers-- Part II. Advanced Properties: 2.1 Basis and subbasis-- 2.2. Product spaces-- 2.3. Relative topology-- 2.4. First countable and second countable-- 2.5. Compactifications-- 2.6. Quotient topologies-- 2.7. Uniformities-- 2.8. Morse theory-- 2.9. Proper mappings-- 2.10. Paracompactness-- Part III. Moore-Smith Convergence and Nets: 3.1. Introductory remarks-- 3.2. Nets-- Part IV. Function Spaces: 4.1. Preliminary ideas-- 4.2. The topology of pointwise convergence-- 4.3. The compact-open topology-- 4.4. Uniform convergence-- 4.5. Equicontinuity and the Ascoli-Arzela theorem-- 4.6. The Weierstrass approximation theorem-- Table of notation-- Glossary-- Bibliography-- Index.
- (source: Nielsen Book Data)9780883853467 20160603
(source: Nielsen Book Data)9780883853467 20160603
- Preface-- Part I. Fundamentals: 1.1. What is topology?-- 1.2. First definitions-- 1.3 Mappings-- 1.4. The separation axioms-- 1.5. Compactness-- 1.6. Homeomorphisms-- 1.7. Connectedness-- 1.8. Path-connectedness-- 1.9. Continua-- 1.10. Totally disconnected spaces-- 1.11. The Cantor set-- 1.12. Metric spaces-- 1.13. Metrizability-- 1.14. Baire's theorem-- 1.15. Lebesgue's lemma and Lebesgue numbers-- Part II. Advanced Properties: 2.1 Basis and subbasis-- 2.2. Product spaces-- 2.3. Relative topology-- 2.4. First countable and second countable-- 2.5. Compactifications-- 2.6. Quotient topologies-- 2.7. Uniformities-- 2.8. Morse theory-- 2.9. Proper mappings-- 2.10. Paracompactness-- Part III. Moore-Smith Convergence and Nets: 3.1. Introductory remarks-- 3.2. Nets-- Part IV. Function Spaces: 4.1. Preliminary ideas-- 4.2. The topology of pointwise convergence-- 4.3. The compact-open topology-- 4.4. Uniform convergence-- 4.5. Equicontinuity and the Ascoli-Arzela theorem-- 4.6. The Weierstrass approximation theorem-- Table of notation-- Glossary-- Bibliography-- Index.
- (source: Nielsen Book Data)9780883853467 20160603
(source: Nielsen Book Data)9780883853467 20160603
Science Library (Li and Ma)
Science Library (Li and Ma) | Status |
---|---|
Stacks | |
QA611 .K683 2009 | Unknown |
- Book
- xii, 107 p. : ill.
- 1. Fundamentals
- 2. Advanced properties of topological spaces
- 3. Moore-Smith convergence and nets
- 4. Function spaces.
- 1. Fundamentals
- 2. Advanced properties of topological spaces
- 3. Moore-Smith convergence and nets
- 4. Function spaces.
- Book
- 1 online resource (218 pages)
Dieses Buch konzentriert das aktuelle Gesamtwissen zum Proximity-Konzept und stellt es dem Leser in gut strukturierter Form dar. Hauptaugenmerk liegt auf den vielfaltigen Moeglichkeiten, die sich aus dem Proximity-Konzept der raumlichen Nahe und seiner Verallgemeinerung im Nearness-Konzept ergeben.
(source: Nielsen Book Data)9783486598605 20180530
(source: Nielsen Book Data)9783486598605 20180530
Dieses Buch konzentriert das aktuelle Gesamtwissen zum Proximity-Konzept und stellt es dem Leser in gut strukturierter Form dar. Hauptaugenmerk liegt auf den vielfaltigen Moeglichkeiten, die sich aus dem Proximity-Konzept der raumlichen Nahe und seiner Verallgemeinerung im Nearness-Konzept ergeben.
(source: Nielsen Book Data)9783486598605 20180530
(source: Nielsen Book Data)9783486598605 20180530
10. A topological aperitif [electronic resource] [2009]
- Book
- ix, 152 p. : ill. ; 24 cm.
- Homeomorphic Sets.- Topological Properties.- Equivalent Subsets.- Surfaces and Spaces.- Polyhedra.- Winding Number.
- (source: Nielsen Book Data)9781848009127 20160605
(source: Nielsen Book Data)9781848009127 20160605
- Homeomorphic Sets.- Topological Properties.- Equivalent Subsets.- Surfaces and Spaces.- Polyhedra.- Winding Number.
- (source: Nielsen Book Data)9781848009127 20160605
(source: Nielsen Book Data)9781848009127 20160605
dx.doi.org SpringerLink
- dx.doi.org SpringerLink
- Google Books (Full view)
11. Topologia [electronic resource] [2008]
- Book
- xii, 297 p. ; 24 cm.
dx.doi.org SpringerLink
- dx.doi.org SpringerLink
- Google Books (Full view)
12. Open problems in topology II [2007]
- Book
- xi, 763 p. : ill. ; 25 cm.
- Part 1. General Topology 1. Selected ordered space problems (H. Bennett and D. Lutzer) 2. Problems on star-covering properties (M. Bonanzinga and M. Matveev) 3. Function space topologies (D.N. Georgiou, S.D. Iliadis and F. Mynard) 4. Spaces and mappings: special networks (C. Liu and Y. Tanaka) 5. Extension problems of real-valued continuous functions (H. Ohta and K. Yamazaki) 6. LE(k)-spaces (O. Okunev) 7. Problems on (ir) resolvability (O. Pavlov) 8. Topological games and Ramsey theory (M. Scheepers) 9. Selection principles and special sets of reals (B. Tsaban) Part 2. Set-theoretic Topology 10. Introduction: Twenty problems in set-theoretic topology (M. Hrusak and J.T. Moore) 11. Thin-tall spaces and cardinal sequences (J. Bagaria) 12. Sequential order (A. Dow) 13. On D-spaces (T. Eisworth) 14. The fourth head of BN (I. Farah) 15. Are stratifiable spaces M1? (G. Gruenhage) 16. Perfect compacta and basis problems in topology (G. Gruenhage and J.T. Moore) 17. Selection problems for hyperspaces (V. Gutev and T. Nogura) 18. Efimov's problem (K.P. Hart) 19. Completely separable MAD families (M. Hrusak and P. Simon) 20. Good, splendid and Jakovlev (I. Juhasz and W.A.R. Weiss) 21. Homogeneous compacta (J. van Mill) 22. Compact spaces with hereditarily normal squares (J.T. Moore) 23. The metrization problem for Frechet groups (J.T. Moore and S. Todorcevic) 24. Cech-Stone remainders of discrete spaces (P.J. Nyikos) 25. First countable, countably compact, noncompact spaces (P.J. Nyikos) 26. Linearly Lindelof problems (E. Pearl) 27. Small Dowker spaces (P.J. Szeptycki) 28. Reflection of topological properties to N1 (F.D. Tall) 29. The Scarborough-Stone problem (J.E. Vaughan) Part 3. Continuum Theory 30. Questions in and out of context (D.P. Bellamy) 31. An update on the elusive fixed-point property (C.L. Hagopian) 32. Hyperspaces of continua (A. Ilanes) 33. Inverse limits and dynamical systems (W.T. Ingram) 34. Indecomposable continua (W. Lewis) 35. Open problems on dendroids (V. Martinez-de-la-Vega and J.M. Martinez-Montejano) 36. -Homogeneous continua (S.B. Nadler, Jr.) 37. Thirty open problems in the theory of homogeneous continua (J.R. Prajs) Part 4. Topological Algebra 38. Problems about the uniform structures of topological groups (A. Bouziad and J-P. Troallic) 39. On some special classes of continuous maps (M.M. Clementino and D. Hofmann) 40. Dense subgroups of compact groups (W.W. Comfort) 41. Selected topics from the structure theory of topological groups (D. Dikranjan and D. Shakhmatov) 42. Recent results and open questions relating Chu duality and Bohr compactifications of locally compact groups (J. Galindo, S. Hernandez and T-S. Wu) 43. Topological transformation groups: selected topics (M. Megrelishvili) 44. Forty-plus annotated questions about large topological groups (V. Pestov) Part 5. Dynamical Systems 45. Minimal flows (W.F. Basener, K. Parwani and T. Wiandt) 46. The dynamics of tiling spaces (A. Clark) 47. Open problems in complex dynam.
- (source: Nielsen Book Data)9780444522085 20160528
(source: Nielsen Book Data)9780444522085 20160528
- Part 1. General Topology 1. Selected ordered space problems (H. Bennett and D. Lutzer) 2. Problems on star-covering properties (M. Bonanzinga and M. Matveev) 3. Function space topologies (D.N. Georgiou, S.D. Iliadis and F. Mynard) 4. Spaces and mappings: special networks (C. Liu and Y. Tanaka) 5. Extension problems of real-valued continuous functions (H. Ohta and K. Yamazaki) 6. LE(k)-spaces (O. Okunev) 7. Problems on (ir) resolvability (O. Pavlov) 8. Topological games and Ramsey theory (M. Scheepers) 9. Selection principles and special sets of reals (B. Tsaban) Part 2. Set-theoretic Topology 10. Introduction: Twenty problems in set-theoretic topology (M. Hrusak and J.T. Moore) 11. Thin-tall spaces and cardinal sequences (J. Bagaria) 12. Sequential order (A. Dow) 13. On D-spaces (T. Eisworth) 14. The fourth head of BN (I. Farah) 15. Are stratifiable spaces M1? (G. Gruenhage) 16. Perfect compacta and basis problems in topology (G. Gruenhage and J.T. Moore) 17. Selection problems for hyperspaces (V. Gutev and T. Nogura) 18. Efimov's problem (K.P. Hart) 19. Completely separable MAD families (M. Hrusak and P. Simon) 20. Good, splendid and Jakovlev (I. Juhasz and W.A.R. Weiss) 21. Homogeneous compacta (J. van Mill) 22. Compact spaces with hereditarily normal squares (J.T. Moore) 23. The metrization problem for Frechet groups (J.T. Moore and S. Todorcevic) 24. Cech-Stone remainders of discrete spaces (P.J. Nyikos) 25. First countable, countably compact, noncompact spaces (P.J. Nyikos) 26. Linearly Lindelof problems (E. Pearl) 27. Small Dowker spaces (P.J. Szeptycki) 28. Reflection of topological properties to N1 (F.D. Tall) 29. The Scarborough-Stone problem (J.E. Vaughan) Part 3. Continuum Theory 30. Questions in and out of context (D.P. Bellamy) 31. An update on the elusive fixed-point property (C.L. Hagopian) 32. Hyperspaces of continua (A. Ilanes) 33. Inverse limits and dynamical systems (W.T. Ingram) 34. Indecomposable continua (W. Lewis) 35. Open problems on dendroids (V. Martinez-de-la-Vega and J.M. Martinez-Montejano) 36. -Homogeneous continua (S.B. Nadler, Jr.) 37. Thirty open problems in the theory of homogeneous continua (J.R. Prajs) Part 4. Topological Algebra 38. Problems about the uniform structures of topological groups (A. Bouziad and J-P. Troallic) 39. On some special classes of continuous maps (M.M. Clementino and D. Hofmann) 40. Dense subgroups of compact groups (W.W. Comfort) 41. Selected topics from the structure theory of topological groups (D. Dikranjan and D. Shakhmatov) 42. Recent results and open questions relating Chu duality and Bohr compactifications of locally compact groups (J. Galindo, S. Hernandez and T-S. Wu) 43. Topological transformation groups: selected topics (M. Megrelishvili) 44. Forty-plus annotated questions about large topological groups (V. Pestov) Part 5. Dynamical Systems 45. Minimal flows (W.F. Basener, K. Parwani and T. Wiandt) 46. The dynamics of tiling spaces (A. Clark) 47. Open problems in complex dynam.
- (source: Nielsen Book Data)9780444522085 20160528
(source: Nielsen Book Data)9780444522085 20160528
www.sciencedirect.com ScienceDirect
- www.sciencedirect.com ScienceDirect
- Google Books (Full view)
SAL3 (off-campus storage)
SAL3 (off-campus storage) | Status |
---|---|
Stacks | Request |
QA611 .O562 2007 | Available |
- Book
- 1 v. (various paging) : ill.
- Book
- 328 p.
- Book
- xiv, 127 p. : ill. (some col.).
- A Crisis in the Experimental Method Archetype-- Orbit Organization in R2 x S1-- Braids as Indicators of Phase-Space Dynamics-- Braids and the Poincare Section-- Reconstruction of Phase-Space Dynamics -- Basic Course-- Reconstruction of Phase-Space Dynamics -- Advanced Course.
- (source: Nielsen Book Data)9789812703804 20160528
(source: Nielsen Book Data)9789812703804 20160528
- A Crisis in the Experimental Method Archetype-- Orbit Organization in R2 x S1-- Braids as Indicators of Phase-Space Dynamics-- Braids and the Poincare Section-- Reconstruction of Phase-Space Dynamics -- Basic Course-- Reconstruction of Phase-Space Dynamics -- Advanced Course.
- (source: Nielsen Book Data)9789812703804 20160528
(source: Nielsen Book Data)9789812703804 20160528
16. Topology [2006]
- Book
- 1 online resource (404 pages)
- PART I: A GEOMETRIC INTRODUCTION TO TOPOLOGY-- PART II: COVERING SPACES, CW COMPLEXES AND HOMOLOGY.
- (source: Nielsen Book Data)9780199202485 20180521
(source: Nielsen Book Data)9780199202485 20180521
- PART I: A GEOMETRIC INTRODUCTION TO TOPOLOGY-- PART II: COVERING SPACES, CW COMPLEXES AND HOMOLOGY.
- (source: Nielsen Book Data)9780199202485 20180521
(source: Nielsen Book Data)9780199202485 20180521
17. Topology : a geometric approach [2003]
- Book
- xv, 388 p. : ill. ; 24 cm.
- PART I: A GEOMETRIC INTRODUCTION TO TOPOLOGY-- PART II: COVERING SPACES, CW COMPLEXES AND HOMOLOGY.
- (source: Nielsen Book Data)9780199202485 20180521
(source: Nielsen Book Data)9780199202485 20180521
- PART I: A GEOMETRIC INTRODUCTION TO TOPOLOGY-- PART II: COVERING SPACES, CW COMPLEXES AND HOMOLOGY.
- (source: Nielsen Book Data)9780199202485 20180521
(source: Nielsen Book Data)9780199202485 20180521
SAL3 (off-campus storage)
SAL3 (off-campus storage) | Status |
---|---|
Stacks | Request |
QA611 .L36 2006 | Available |
18. A taste of topology [2005]
- Book
- x, 176 p. : ill., map ; 23 cm.
- Preface.- Introduction.- Set Theory.- Metric Spaces.- Set Theoretic Topology.- Systems of Continuous Functions.- Basic Algebraic Topology.- The Classical Mittag-Leffler Theorem Derived from Bourbaki?s.- Failure of the Heine-Borel Theorem in Infinite-Dimensional Spaces.- The Arzela-Ascoli Theorem.- References.- List of Symbols.- Index.
- (source: Nielsen Book Data)9780387257907 20160528
(source: Nielsen Book Data)9780387257907 20160528
- Preface.- Introduction.- Set Theory.- Metric Spaces.- Set Theoretic Topology.- Systems of Continuous Functions.- Basic Algebraic Topology.- The Classical Mittag-Leffler Theorem Derived from Bourbaki?s.- Failure of the Heine-Borel Theorem in Infinite-Dimensional Spaces.- The Arzela-Ascoli Theorem.- References.- List of Symbols.- Index.
- (source: Nielsen Book Data)9780387257907 20160528
(source: Nielsen Book Data)9780387257907 20160528
SAL3 (off-campus storage)
SAL3 (off-campus storage) | Status |
---|---|
Stacks | Request |
QA611 .R85 2005 | Available |
19. Computational Homology [2004]
- Book
- 1 online resource (497 pages)
- Preface Part I Homology 1 Preview 1.1 Analyzing Images 1.2 Nonlinear Dynamics 1.3 Graphs 1.4 Topological and Algebraic Boundaries 1.5 Keeping Track of Directions 1.6 Mod 2 Homology of Graphs 2 Cubical Homology 2.1 Cubical Sets 2.1.1 Elementary Cubes 2.1.2 Cubical Sets 2.1.3 Elementary Cells 2.2 The Algebra of Cubical Sets 2.2.1 Cubical Chains 2.2.2 Cubical Chains in a Cubical Set 2.2.3 The Boundary Operator 2.2.4 Homology of Cubical Sets 2.3 Connected Components and H0(X) 2.4 Elementary Collapses 2.5 Acyclic Cubical Spaces 2.6 Homology of Abstract Chain Complexes 2.7 Reduced Homology 2.8 Bibliographical Remarks 3 Computing Homology Groups 3.1 Matrix Algebra over Z 3.2 Row Echelon Form 3.3 Smith Normal Form 3.4 Structure of Abelian Groups 3.5 Computing Homology Groups 3.6 Computing Homology of Cubical Sets 3.7 Preboundary of a Cycle-Algebraic Approach 3.8 Bibliographical Remarks 4 Chain Maps and Reduction Algorithms 4.1 Chain Maps 4.2 Chain Homotopy 4.3 Internal Elementary Reductions 4.3.1 Elementary Collapses Revisited 4.3.2 Generalization of Elementary Collapses 4.4 CCR Algorithm 4.5 Bibliographical Remarks 5 PreviewofMaps 5.1 Rational Functions and Interval Arithmetic 5.2 Maps on an Interval 5.3 Constructing Chain Selectors 5.4 Maps of A1 6 Homology of Maps 6.1 Representable Sets 6.2 Cubical Multivalued Maps 6.3 Chain Selectors 6.4 Homology of Continuous Maps 6.4.1 Cubical Representations 6.4.2 Rescaling 6.5 Homotopy Invariance 6.6 Bibliographical Remarks 7 Computing Homology of Maps 7.1 Producing Multivalued Representation 7.2 Chain Selector Algorithm 7.3 Computing Homology of Maps 7.4 Geometric Preboundary Algorithm (optional section) 7.5 Bibliographical Remarks Part II Extensions 8 Prospects in Digital Image Processing 8.1 Images and Cubical Sets 8.2 Patterns from Cahn-Hilliard 8.3 Complicated Time-Dependent Patterns 8.4 Size Function 8.5 Bibliographical Remarks 9 Homological Algebra 9.1 Relative Homology 9.1.1 Relative Homology Groups 9.1.2 Maps in Relative Homology 9.2 Exact Sequences 9.3 The Connecting Homomorphism 9.4 Mayer-Vietoris Sequence 9.5 Weak Boundaries 9.6 Bibliographical Remarks 10 Nonlinear Dynamics 10.1 Maps and Symbolic Dynamics 10.2 Differential Equations and Flows 10.3 Wayzewski Principle 10.4 Fixed-Point Theorems 10.4.1 Fixed Points in the Unit Ball 10.4.2 The Lefschetz Fixed-Point Theorem 10.5 Degree Theory 10.5.1 Degree on Spheres 10.5.2 Topological Degree 10.6 Complicated Dynamics 10.6.1 Index Pairs and Index Map 10.6.2 Topological Conjugacy 10.7 Computing Chaotic Dynamics 10.8 Bibliographical Remarks 11 Homology of Topological Polyhedra 11.1 Simplicial Homology 11.2 Comparison of Cubical and Simplicial Complexes 11.3 Homology Functor 11.3.1 Category of Cubical Sets 11.3.2 Connected Simple Systems 11.4 Bibliographical Remarks Part III Tools from Topology and Algebra 12 Topology 12.1 Norms and Metrics in Rd 12.2 Topology 12.3 Continuous Maps 12.4 Connectedness 12.5 Limits and Compactness 13 Algebra 13.1 Abelian Groups 13.1.1 Algebraic Operations 13.1.2 Groups 13.1.3 Cyclic Groups and Torsion Subgroup 13.1.4 Quotient Groups 13.1.5 Direct Sums 13.2 Fields and Vector Spaces 13.2.1 Fields 13.2.2 Vector Spaces 13.2.3 Linear Combinations and Bases 13.3 Homomorphisms 13.3.1 Homomorphisms of Groups 13.3.2 Linear Maps 13.3.3 Matrix Algebra 13.4 Free Abelian Groups 13.4.1 Bases in Groups 13.4.2 Subgroups of Free Groups 13.4.3 Homomorphisms of Free Groups 14 Syntax of Algorithms 14.1 Overview 14.2 Data Structures 14.2.1 Elementary Data Types 14.2.2 Lists 14.2.3 Arrays 14.2.4 Vectors and Matrices 14.2.5 Sets.
- (source: Nielsen Book Data)9781441923547 20180521
(source: Nielsen Book Data)9781441923547 20180521
- Preface Part I Homology 1 Preview 1.1 Analyzing Images 1.2 Nonlinear Dynamics 1.3 Graphs 1.4 Topological and Algebraic Boundaries 1.5 Keeping Track of Directions 1.6 Mod 2 Homology of Graphs 2 Cubical Homology 2.1 Cubical Sets 2.1.1 Elementary Cubes 2.1.2 Cubical Sets 2.1.3 Elementary Cells 2.2 The Algebra of Cubical Sets 2.2.1 Cubical Chains 2.2.2 Cubical Chains in a Cubical Set 2.2.3 The Boundary Operator 2.2.4 Homology of Cubical Sets 2.3 Connected Components and H0(X) 2.4 Elementary Collapses 2.5 Acyclic Cubical Spaces 2.6 Homology of Abstract Chain Complexes 2.7 Reduced Homology 2.8 Bibliographical Remarks 3 Computing Homology Groups 3.1 Matrix Algebra over Z 3.2 Row Echelon Form 3.3 Smith Normal Form 3.4 Structure of Abelian Groups 3.5 Computing Homology Groups 3.6 Computing Homology of Cubical Sets 3.7 Preboundary of a Cycle-Algebraic Approach 3.8 Bibliographical Remarks 4 Chain Maps and Reduction Algorithms 4.1 Chain Maps 4.2 Chain Homotopy 4.3 Internal Elementary Reductions 4.3.1 Elementary Collapses Revisited 4.3.2 Generalization of Elementary Collapses 4.4 CCR Algorithm 4.5 Bibliographical Remarks 5 PreviewofMaps 5.1 Rational Functions and Interval Arithmetic 5.2 Maps on an Interval 5.3 Constructing Chain Selectors 5.4 Maps of A1 6 Homology of Maps 6.1 Representable Sets 6.2 Cubical Multivalued Maps 6.3 Chain Selectors 6.4 Homology of Continuous Maps 6.4.1 Cubical Representations 6.4.2 Rescaling 6.5 Homotopy Invariance 6.6 Bibliographical Remarks 7 Computing Homology of Maps 7.1 Producing Multivalued Representation 7.2 Chain Selector Algorithm 7.3 Computing Homology of Maps 7.4 Geometric Preboundary Algorithm (optional section) 7.5 Bibliographical Remarks Part II Extensions 8 Prospects in Digital Image Processing 8.1 Images and Cubical Sets 8.2 Patterns from Cahn-Hilliard 8.3 Complicated Time-Dependent Patterns 8.4 Size Function 8.5 Bibliographical Remarks 9 Homological Algebra 9.1 Relative Homology 9.1.1 Relative Homology Groups 9.1.2 Maps in Relative Homology 9.2 Exact Sequences 9.3 The Connecting Homomorphism 9.4 Mayer-Vietoris Sequence 9.5 Weak Boundaries 9.6 Bibliographical Remarks 10 Nonlinear Dynamics 10.1 Maps and Symbolic Dynamics 10.2 Differential Equations and Flows 10.3 Wayzewski Principle 10.4 Fixed-Point Theorems 10.4.1 Fixed Points in the Unit Ball 10.4.2 The Lefschetz Fixed-Point Theorem 10.5 Degree Theory 10.5.1 Degree on Spheres 10.5.2 Topological Degree 10.6 Complicated Dynamics 10.6.1 Index Pairs and Index Map 10.6.2 Topological Conjugacy 10.7 Computing Chaotic Dynamics 10.8 Bibliographical Remarks 11 Homology of Topological Polyhedra 11.1 Simplicial Homology 11.2 Comparison of Cubical and Simplicial Complexes 11.3 Homology Functor 11.3.1 Category of Cubical Sets 11.3.2 Connected Simple Systems 11.4 Bibliographical Remarks Part III Tools from Topology and Algebra 12 Topology 12.1 Norms and Metrics in Rd 12.2 Topology 12.3 Continuous Maps 12.4 Connectedness 12.5 Limits and Compactness 13 Algebra 13.1 Abelian Groups 13.1.1 Algebraic Operations 13.1.2 Groups 13.1.3 Cyclic Groups and Torsion Subgroup 13.1.4 Quotient Groups 13.1.5 Direct Sums 13.2 Fields and Vector Spaces 13.2.1 Fields 13.2.2 Vector Spaces 13.2.3 Linear Combinations and Bases 13.3 Homomorphisms 13.3.1 Homomorphisms of Groups 13.3.2 Linear Maps 13.3.3 Matrix Algebra 13.4 Free Abelian Groups 13.4.1 Bases in Groups 13.4.2 Subgroups of Free Groups 13.4.3 Homomorphisms of Free Groups 14 Syntax of Algorithms 14.1 Overview 14.2 Data Structures 14.2.1 Elementary Data Types 14.2.2 Lists 14.2.3 Arrays 14.2.4 Vectors and Matrices 14.2.5 Sets.
- (source: Nielsen Book Data)9781441923547 20180521
(source: Nielsen Book Data)9781441923547 20180521
20. Fixed Point Theory [2003]
- Book
- 1 online resource (700 pages)
- Elementary Fixed Point Theorems * Theorem of Borsuk and Topological Transversality * Homology and Fixed Points * Leray-Schauder Degree and Fixed Point Index * The Lefschetz-Hopf Theory * Selected Topics * Index.
- (source: Nielsen Book Data)9781441918055 20180521
(source: Nielsen Book Data)9781441918055 20180521
- Elementary Fixed Point Theorems * Theorem of Borsuk and Topological Transversality * Homology and Fixed Points * Leray-Schauder Degree and Fixed Point Index * The Lefschetz-Hopf Theory * Selected Topics * Index.
- (source: Nielsen Book Data)9781441918055 20180521
(source: Nielsen Book Data)9781441918055 20180521
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