LEADER 03044nam 22008055 450 001 996466031903316 005 20230406054232.0 010 $a3-540-46485-9 024 7 $a10.1007/11893295 035 $a(CKB)1000000000283943 035 $a(SSID)ssj0000319144 035 $a(PQKBManifestationID)11223629 035 $a(PQKBTitleCode)TC0000319144 035 $a(PQKBWorkID)10336535 035 $a(PQKB)10852768 035 $a(DE-He213)978-3-540-46485-3 035 $a(MiAaPQ)EBC3066622 035 $a(MiAaPQ)EBC6693554 035 $a(Au-PeEL)EBL6693554 035 $a(PPN)12313904X 035 $a(EXLCZ)991000000000283943 100 $a20100301d2006 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aNeural Information Processing$b[electronic resource] $e13th International Conference, ICONIP 2006, Hong Kong, China, October 3-6, 2006, Proceedings, Part III /$fedited by Jun Wang, Laiwan Chan, DeLiang Wang 205 $a1st ed. 2006. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2006. 215 $a1 online resource (XXII, 1227 p.) 225 1 $aTheoretical Computer Science and General Issues,$x2512-2029 ;$v4234 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-46484-0 320 $aIncludes bibliographical references and indexes. 327 $aBioinformatics and Biomedical Applications -- Information Security -- Data and Text Processing -- Financial Applications -- Manufacturing Systems -- Control and Robotics -- Evolutionary Algorithms and Systems -- Fuzzy Systems -- Hardware Implementations. 410 0$aTheoretical Computer Science and General Issues,$x2512-2029 ;$v4234 606 $aArtificial intelligence 606 $aComputer science 606 $aInformation technology?Management 606 $aApplication software 606 $aDatabase management 606 $aComputer vision 606 $aArtificial Intelligence 606 $aTheory of Computation 606 $aComputer Application in Administrative Data Processing 606 $aComputer and Information Systems Applications 606 $aDatabase Management 606 $aComputer Vision 615 0$aArtificial intelligence. 615 0$aComputer science. 615 0$aInformation technology?Management. 615 0$aApplication software. 615 0$aDatabase management. 615 0$aComputer vision. 615 14$aArtificial Intelligence. 615 24$aTheory of Computation. 615 24$aComputer Application in Administrative Data Processing. 615 24$aComputer and Information Systems Applications. 615 24$aDatabase Management. 615 24$aComputer Vision. 676 $a006.32 702 $aKing$b Irwin$f1961- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466031903316 996 $aNeural Information Processing$92554499 997 $aUNISA LEADER 05467nam 22004573 450 001 996466400803316 005 20230421105531.0 010 $a3-030-70608-7 035 $a(CKB)5590000000487489 035 $a(MiAaPQ)EBC6644887 035 $a(Au-PeEL)EBL6644887 035 $a(OCoLC)1257548822 035 $a(PPN)269152725 035 $a(EXLCZ)995590000000487489 100 $a20210901d2021 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAlgebraic Topology 210 1$aCham :$cSpringer International Publishing AG,$d2021. 210 4$d©2021. 215 $a1 online resource (216 pages) 311 $a3-030-70607-9 327 $aIntro -- Foreword -- Introduction -- Contents -- 1 Surface Preliminaries -- 1.1 Surfaces -- 1.2 Euclidean Space -- 1.3 Open Sets -- 1.4 Functions and Their Properties -- 1.5 Continuity -- 1.6 Problems -- 2 Surfaces -- 2.1 The Definition of a Surface -- 2.2 Examples of Surfaces -- 2.3 Spheres as Surfaces -- 2.4 Surfaces with Boundary -- 2.5 Closed, Bounded, and Compact Surfaces -- 2.6 Equivalence Relations and Topological Equivalence -- 2.7 Homeomorphic Spaces -- 2.8 Invariants -- 2.9 Problems -- 3 The Euler Characteristic and Identification Spaces -- 3.1 Triangulations and the Euler Characteristic -- 3.2 Invariance of the Euler Characteristic -- 3.3 Identification Spaces -- 3.4 ID Spaces as Surfaces -- 3.5 Abstract Topological Spaces -- 3.6 The Quotient Topology -- 3.7 Further Examples of ID Spaces -- 3.8 Triangulations of ID Spaces -- 3.9 The Connected Sum -- 3.10 The Euler Characteristic of a Compact Surface with Boundary -- 3.11 Problems -- 4 Classification Theorem of Compact Surfaces -- 4.1 The Geometry of the Projective Plane and the Klein Bottle -- 4.2 Orientable and Nonorientable Surfaces -- 4.3 The Classification Theorem for Compact Surfaces -- 4.4 Compact Surfaces Have Finite Triangulations -- 4.5 Proof of the Classification Theorem -- 4.6 Problems -- 5 Introduction to Group Theory -- 5.1 Why Use Groups? -- 5.2 A Motivating Example -- 5.3 Definition of a Group -- 5.4 Examples of Groups -- 5.5 Free Groups, Generators, and Relations -- 5.6 Free Products -- 5.7 Problems -- 6 Structure of Groups -- 6.1 Subgroups -- 6.2 Direct Products of Groups -- 6.3 Homomorphisms -- 6.4 Isomorphisms -- 6.5 Existence of Homomorphisms -- 6.6 Finitely Generated Abelian Groups -- 6.7 Problems -- 7 Cosets, Normal Subgroups, and Quotient Groups -- 7.1 Cosets -- 7.2 Lagrange's Theorem and Its Consequences -- 7.3 Coset Spaces and Quotient Groups. 327 $a7.4 Properties and Examples of Normal Subgroups -- 7.5 Coset Representatives -- 7.6 A Quotient of a Dihedral Group -- 7.7 Building up Finite Groups -- 7.8 An Isomorphism Theorem -- 7.9 Problems -- 8 The Fundamental Group -- 8.1 Paths and Loops on a Surface -- 8.2 Equivalence of Paths and Loops -- 8.3 Equivalence Classes of Paths and Loops -- 8.4 Multiplication of Path and Loop Classes -- 8.5 Definition of the Fundamental Group -- 8.6 Problems -- 9 Computing the Fundamental Group -- 9.1 Homotopies of Maps and Spaces -- 9.2 Computing the Fundamental Group of a Circle -- 9.3 Problems -- 10 Tools for Fundamental Groups -- 10.1 More Fundamental Groups -- 10.2 The Degree of a Loop -- 10.3 Fundamental Group of a Circle-Redux -- 10.4 The Induced Homomorphism on Fundamental Groups -- 10.5 Retracts -- 10.6 Problems -- 11 Applications of Fundamental Groups -- 11.1 The Fundamental Theorem of Algebra -- 11.2 Further Applications of the Fundamental Group -- 11.3 Problems -- 12 The Seifert-Van Kampen Theorem -- 12.1 Wedges of circles -- 12.2 The Seifert-Van Kampen Theorem: First Version -- 12.3 More Fundamental Groups -- 12.4 The Seifert-Van Kampen Theorem: Second Version -- 12.5 The Fundamental Group of a Compact Surface -- 12.6 Even More Fundamental Groups -- 12.7 Proof of the Second Version of the Seifert-Van Kampen Theorem -- 12.8 General Seifert-Van Kampen Theorem -- 12.9 Groups as Fundamental Groups -- 12.10 Problems -- 13 Introduction to Homology -- 13.1 The Idea of Homology -- 13.2 Chains -- 13.3 The Boundary Map -- 13.4 Homology -- 13.5 The Zeroth Homology Group -- 13.6 Homology of the Klein Bottle -- 13.7 Homology and Euler Characteristic -- 13.8 Homology and Orientability -- 13.9 Smith Normal Form -- 13.10 The Induced Map on Homology -- 13.11 Problems -- 14 The Mayer-Vietoris Sequence -- 14.1 Exact Sequences -- 14.2 The Mayer-Vietoris Sequence. 327 $a14.3 Homology of Orientable Surfaces -- 14.4 The Jordan Curve Theorem -- 14.5 The Hurewicz Map -- 14.6 Problems -- Correction to: The Seifert-Van Kampen Theorem -- Correction to: Chapter 12 in: C. Bray et al., Algebraic Topology, https://doi.org/10.1007/978-3-030-70608-112 -- Appendix A Topological Notions -- A.1 Compactness Results -- A.2 Technical Conditions for Abstract Surfaces -- Appendix B A Brief Look at Singular Homology -- Appendix C Hints for Selected Problems -- Appendix References -- -- Index. 606 $aTopologia algebraica$2thub 608 $aLlibres electrònics$2thub 615 7$aTopologia algebraica 700 $aBray$b Clark$0971535 701 $aButscher$b Adrian$0971536 701 $aRubinstein-Salzedo$b Simon$0768226 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466400803316 996 $aAlgebraic Topology$92208891 997 $aUNISA