General topology. Reprint of the 1970 original. (English) Zbl 1052.54001

Willard, Stephen

Mineola, NY: Dover Publications (ISBN 0-486-43479-6/pbk ). xii, 369 p. (2004).

Dover has chosen well in deciding to reproduce unabridged the 1970 edition of this excellent text a third of a century on. Of course in the meantime there have been advances in some aspects of General Topology, especially in the now tremendously developed field of Set-Theoretic Topology. However, this book still provides the reader (most likely a beginning graduate student) with a thorough introduction to a wide range of important topics almost all of which should be familiar to anyone taking topology seriously. The chapter headings give some indication of this range: Set Theory and Metric Spaces; Topological Spaces; New Spaces from Old; Convergence; Separation and Countability; Compactness; Metrizable Spaces; Connectedness; Uniform Spaces; Function Spaces. Included in the chapter on connectedness is a section on the fundamental group and an evaluation of \(\pi_1\mathbb S^1\) is given. Some especially attractive features of the book are the comprehensive collection of exercises at the end of each section, the 25 pages of historical notes, the bibliography of about 500 items, which must include all of the important papers in General Topology up until then, and the index of about 2000 items. The referencing system used in the index is somewhat annoying: a particular definition, result or problem is cited by item number instead of page, which is attractive, but hunting for the citation is hindered as the section numbers are hidden in the inside top corner of the pages.

Reviewer: David B. Gauld (Auckland)

MSC:

54-01

Introductory exposition (textbooks, tutorial papers, etc.) pertaining to general topology

Keywords:

metric spaces; topological spaces; convergence; separation; countability; compactness; metrizable spaces; connectedness; uniform spaces; function spaces

Citations:

Zbl 0205.26601