Introduction to Topology

Cover ......Page 1 Short title ......Page 2 Title page ......Page 3 Copyright ......Page 4 Preface ......Page 5 Contents ......Page 7 1 Introduction ......Page 10 2 Sets and subsets ......Page 13 3 Set operations: union, intersection, and complements ......Page 16 4 Indexed families of sets ......Page 19 5 Products of sets ......Page 22 6 Functions ......Page 24 7 Composition of functions and diagrams ......Page 29 8 Inverse functions ......Page 35 9 Restriction and extension of functions ......Page 38 1 Introduction ......Page 41 2 Metric spaces ......Page 42 3 Continuity ......Page 48 4 Open spheres and neighborhoods ......Page 53 5 Open sets ......Page 61 6 Limit points ......Page 65 7 Closed sets ......Page 69 8 Products ......Page 74 9 Subspaces ......Page 80 10 Equivalence of metric spaces ......Page 84 1 Introduction ......Page 92 2 Topological spaces ......Page 93 3 Neighborhoods and neighborhood spaces ......Page 97 4 Closure, interior, boundary ......Page 104 5 Functions, continuity, homeomorphism ......Page 112 6 Subspaces ......Page 117 7 Products ......Page 121 1 Introduction ......Page 125 2 Connectedness ......Page 126 3 Connectedness on the real line ......Page 131 4 Some applications of connectedness ......Page 134 5 Components and local connectedness ......Page 143 6 Arcwise connected topological spaces ......Page 147 7 Homotopic paths ......Page 153 8 Simple connectedness ......Page 162 1 Introduction ......Page 171 2 Compact topological spaces ......Page 172 3 Compact subsets of the real line ......Page 180 4 Products of compact spaces ......Page 183 5 Compact metric spaces ......Page 187 6 Compactness and the Bolzano-Weierstrass property ......Page 195 7 Identification topologies and spaces ......Page 202 Bibliography ......Page 220 Special Symbols ......Page 221 Index ......Page 224