Synopses & Reviews
Highly regarded for its exceptional clarity, imaginative and instructive exercises, and fine writing style, this concise book offers an ideal introduction to the fundamentals of topology. It provides a simple, thorough survey of elementary topics, starting with set theory and advancing to metric and topological spaces, connectedness, and compactness. 1975 edition.
An undergraduate introduction to the fundamentals of topology engagingly written, filled with helpful insights, complete with many stimulating and imaginative exercises to help students develop a solid grasp of the subject.
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.
Includes bibliographical references (p. 201-202) and index.
Table of Contents
1 Theory of Sets
2 Sets and subsets
3 "Set operations: union, intersection, and complement"
4 Indexed families of sets
5 Products of sets
8 Composition of functions and diagrams
9 "Inverse functions, extensions, and restrictions"
10 Arbitrary products
2 Metric Spaces
2 Metric spaces
4 Open balls and neighborhoods
6 Open sets and closed sets
7 Subspaces and equivalence of metric spaces
8 An infinite dimensional Euclidean space
3 Topological Spaces
2 Topological spaces
3 Neighborhoods and neighborhood spaces
4 "Closure, interior, boundary"
5 "Functions, continuity, homeomorphism"
8 Identification topologies
9 Categories and functors
3 Connectedness on the real line
4 Some applications of connectedness
5 Components and local connectedness
6 Path-connected topological spaces
7 Homotopic paths and the fundamental group
8 Simple connectedness
2 Compact topological spaces
3 Compact subsets of the real line
4 Products of compact spaces
5 Compact metric spaces
6 Compactness and the Bolzano-Weierstrass property
7 Surfaces by identification