»ù±¾ÍØÆËѧBasic topology

Preface Chapter 1 Introduction 1.Euler's theorem 2.Topological equivalence 3.Surfaces 4.Abstract spaces 5.A classification theorem 6.Topological invariants Chapter 2 Continuity 1.Open and closed sets 2.Continuous functions 3.A space-filling curve 4.The Tietze extension theorem Chapter 3 Compactness and connectedness 1.Closed bounded subsets of En 2.The Heine-Borel theorem 3.Properties of compact spaces 4.Product spaces 5.Connectedness 6.Joining points by paths Chapter 4 Identification spaces 1.Constructing a Mobius strip 2.The identification topology 3.Topological groups 4.Orbit spaces Chapter 5 The fundamental group 1.Homotopic maps 2.Construction of the fundamental group 3.Calculations 4.Homotopy type 5.The Brouwer fixed-point theorem 6.Separation of the plane 7.The boundary of a surface Chapter 6 Triangulations 1.Triangulating spaces 2.Barycentric subdivision 3.Simplicial approximation 4.The edge group of a complex 5.Triangulating orbit spaces 6.Infinite complexes Chapter 7 Surfaces 1.Classification 2.Triangulation and orientation 3.Euler characteristics 4.Surgery 5.Surface symbols Chapter 8 Simplicial homology 1.Cycles and boundaries 2.Homology groups 3.Examples 4.Simplicial maps 5.Stellar subdivision 6.Invariance Chapter 9 Degree and Lefschetz number 1.Maps of spheres 2.The Euler-Poincare formula 3.The Borsuk-Ulam theorem 4.The Lefschetz fixed-point theorem 5.Dimension Chapter 10 Knots and covering spaces 1.Examples of knots 2.The knot group 3.Seifert surfaces 4.Covering spaces 5.The Alexander polynomial Appendix: Generators and relations Bibliography Index