Concise undergraduate introduction to fundamentals of topology -- clearly and engagingly written, and filled with stimulating, imaginative exercises. Topics include set theory, metric and topological spaces, connectedness, and compactness. 1975 edition.
Preface1 Theory of Sets1 Introduction2 Sets and subsets3 "Set operations: union, intersection, and complement"4 Indexed families of sets5 Products of sets6 Functions7 Relations8 Composition of functions and diagrams9 "Inverse functions, extensions, and restrictions"10 Arbitrary products2 Metric Spaces1 Introduction2 Metric spaces3 Continuity4 Open balls and neighborhoods5 Limits6 Open sets and closed sets7 Subspaces and equivalence of metric spaces8 An infinite dimensional Euclidean space3 Topological Spaces1 Introduction2 Topological spaces3 Neighborhoods and neighborhood spaces4 "Closure, interior, boundary"5 "Functions, continuity, homeomorphism"6 Subspaces7 Products8 Identification topologies9 Categories and functors4 Connectedness1 Introduction2 Connectedness3 Connectedness on the real line4 Some applications of connectedness5 Components and local connectedness6 Path-connected topological spaces7 Homotopic paths and the fundamental group8 Simple connectedness5 Compactness1 Introduction2 Compact topological spaces3 Compact subsets of the real line4 Products of compact spaces5 Compact metric spaces6 Compactness and the Bolzano-Weierstrass property7 Surfaces by identificationBibliographyIndex
Preface1 Theory of Sets1 Introduction2 Sets and subsets3 "Set operations: union, intersection, and complement"4 Indexed families of sets5 Products of sets6 Functions7 Relations8 Composition of functions and diagrams9 "Inverse functions, extensions, and restrictions"10 Arbitrary products2 Metric Spaces1 Introduction2 Metric spaces3 Continuity4 Open balls and neighborhoods5 Limits6 Open sets and closed sets7 Subspaces and equivalence of metric spaces8 An infinite dimensional Euclidean space3 Topological Spaces1 Introduction2 Topological spaces3 Neighborhoods and neighborhood spaces4 "Closure, interior, boundary"5 "Functions, continuity, homeomorphism"6 Subspaces7 Products8 Identification topologies9 Categories and functors4 Connectedness1 Introduction2 Connectedness3 Connectedness on the real line4 Some applications of connectedness5 Components and local connectedness6 Path-connected topological spaces7 Homotopic paths and the fundamental group8 Simple connectedness5 Compactness1 Introduction2 Compact topological spaces3 Compact subsets of the real line4 Products of compact spaces5 Compact metric spaces6 Compactness and the Bolzano-Weierstrass property7 Surfaces by identificationBibliographyIndex
