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.

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