Foundations of topology. (English) Zbl 0931.54001

Patty, C. Wayne

Boston, MA: PWS-KENT Publishing Company. x, 349 p. (1993).

This book is a clear and systematic topology text at the upper division or beginning graduate level. The first five chapters deal with traditional topics of general topology (topological and metric spaces; connectedness and compactness; separation and countability axioms). Chapter 6 uses contraction mappings in metric spaces as the starting point for a discussion of normed linear spaces, Fréchet derivatives of mappings between Banach spaces, the inverse and implicit function theorems in the Banach space setting, simple examples of differential manifolds, and fractals (Mandelbrot and Julia sets; Hausdorff dimension). Chapter 7 is on paracompactness and metrization theorems. Chapter 8 discusses the fundamental group, covering spaces, and knots. Chapter 9, “Applications of homotopy”, includes proofs of the fundamental theorem of algebra and the Jordan curve theorem. Nine brief appendices provide background material on logic and proofs, basic topics in set theory, cardinal and ordinal numbers, and basic abstract algebra. All mathematics majors will find this book interesting and valuable.

Reviewer: Perry Smith (MR 94d:54002)

MSC:

54-01

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