Willard S. General Topology

Dover Publications, 2004. — 369 p. — ISBN 13 9780486434797.This book is designed to develop the fundamental concepts of general topology which are the basic tools of working mathematicians in a variety of fields. The material here is sufficient for a variety of one- or two-semester courses, and presupposes a student who has successfully mastered the material of a rigorous course in advanced calculus or real analysis. Thus it is addressed primarily to the beginning graduate student and the good undergraduate.Set Theory and Metric Spaces
Topological Spaces
New Spaces from Old
Convergence
Separation and Countability
Compactness
Metrizable Spaces
Connectedness
Uniform Spaces
Function Spaces
Historical Notes