Introduction to Topology / Edition 3

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Overview

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.

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Product Details

  • ISBN-13: 9780486663524
  • Publisher: Dover Publications
  • Publication date: 7/1/1990
  • Series: Dover Books on Mathematics Series
  • Edition description: REV
  • Edition number: 3
  • Pages: 224
  • Sales rank: 622,799
  • Product dimensions: 5.44 (w) x 8.41 (h) x 0.45 (d)

Table of Contents

Preface
1 Theory of Sets
  1 Introduction
  2 Sets and subsets
  3 "Set operations: union, intersection, and complement"
  4 Indexed families of sets
  5 Products of sets
  6 Functions
  7 Relations
  8 Composition of functions and diagrams
  9 "Inverse functions, extensions, and restrictions"
  10 Arbitrary products
2 Metric Spaces
  1 Introduction
  2 Metric spaces
  3 Continuity
  4 Open balls and neighborhoods
  5 Limits
  6 Open sets and closed sets
  7 Subspaces and equivalence of metric spaces
  8 An infinite dimensional Euclidean space
3 Topological Spaces
  1 Introduction
  2 Topological spaces
  3 Neighborhoods and neighborhood spaces
  4 "Closure, interior, boundary"
  5 "Functions, continuity, homeomorphism"
  6 Subspaces
  7 Products
  8 Identification topologies
  9 Categories and functors
4 Connectedness
  1 Introduction
  2 Connectedness
  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
5 Compactness
  1 Introduction
  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
Bibliography
Index
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  • Anonymous

    Posted April 29, 2011

    metric spaces

    =metric spaces

    0 out of 1 people found this review helpful.

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