トポロジー入門 Elements of Topology

Singh, Tej Bahadur

Chapman & Hall（2013/05発売）

• 製本 Hardcover:ハードカバー版／ページ数 530 p.／サイズ 50 illus.
• 言語 ENG
• 商品コード 9781439871959
• DDC分類 514

基本説明

Based on the author's more than two decades of teaching experience, this text provides a streamlined introduction to topology, including algebraic and point-set topology.

Full Description

Topology is a large subject with many branches broadly categorized as algebraic topology, point-set topology, and geometric topology. Point-set topology is the main language for a broad variety of mathematical disciplines. Algebraic topology serves as a powerful tool for studying the problems in geometry and numerous other areas of mathematics. Elements of Topology provides a basic introduction to point-set topology and algebraic topology. It is intended for advanced undergraduate and beginning graduate students with working knowledge of analysis and algebra. Topics discussed include the theory of convergence, function spaces, topological transformation groups, fundamental groups, and covering spaces.The author makes the subject accessible by providing more than 250 worked examples and counterexamples with applications. The text also includes numerous end-of-section exercises to put the material into context.

Contents

Topological SpacesMetric Spaces Topologies Derived Concepts Bases Subspaces Continuity and ProductsContinuityProduct TopologyConnectednessConnected Spaces Components Path-Connected Spaces Local ConnectivityConvergence Sequences Nets Filters Hausdorff SpacesCountability Axioms 1st and 2nd Countable Spaces Separable and Lindeloef SpacesCompactnessCompact Spaces Countably Compact Spaces Compact Metric Spaces Locally Compact Spaces Proper Maps Topological Constructions Quotient Spaces Identification Maps Cones, Suspensions and Joins Wedge Sums and Smash Products Adjunction Spaces Coherent TopologiesSeparation AxiomsRegular Spaces Normal Spaces Completely Regular Spaces Stone-Cech CompactificationParacompactness and MetrizabilityParacompact Spaces A Metrization TheoremCompleteness Complete Spaces Completion Baire Spaces Function Spaces Topology of Pointwise ConvergenceCompact-Open Topology Topology of Compact Convergence Topological Groups Examples and Basic PropertiesSubgroups Isomorphisms Direct ProductsTransformation GroupsGroup ActionsOrbit SpacesThe Fundamental Group Homotopic Maps The Fundamental GroupFundamental Groups of SpheresThe Seifert-van Kampen Theorem Covering Spaces Covering Maps The Lifting Problem The Universal Covering Spaces Deck Transformations The Existence of Covering Spaces Appendix A: Set Theory Appendix B: Fields R, C and H BibliographyIndex