General Topology

"An elegant piece of work, suitable as a text for the beginning student as well as pleasant and informative reading for the mature mathematician." — Scripta Mathematica

This critically acclaimed text by a major twentieth-century mathematician presents a detailed theory of Fréchet (V) spaces and a comprehensive examination of their relevance to topological spaces, plus in-depth discussions of metric and complete spaces. The author's exposition is clear and refined. Moreover, his axiomatic treatment of the theory of point sets, apart from its logical simplicity, has also an advantage: it supplies excellent material for exercise in abstract thinking and logical argument in the deduction of theorems from stated suppositions alone — that is, in proving theorems by drawing on strictly logical conclusions, without appeal to intuition. Numerous worked and unworked examples supplement each chapter.

Waclaw Sierpinski (1882–1969) was a prominent Polish mathematician and the author of 50 books and over 700 papers. His major contributions were in the areas of set theory, number theory, the theory of functions, and topology. He was for most of his life on the faculty of the University of Warsaw. Dover also publishes his Pythagorean Triangles.

Author's Preface
Translator's Preface
I. Frechet (V) Spaces
II. Topological Spaces
III.  Topological Spaces With a Countable Basis
IV.  Hausdorff Topological Spaces Satisfying the First Axiom of Countability
V. Normal Topological Spaces
VI. Metric Spaces
VII. Complete Spaces
Appendix
Notes 
Index