Metric Spaces

Cambridge Tracts in Mathematics #57

by E.T. Copson

Metric space topology, as the generalization to abstract spaces of the theory of sets of points on a line or in a plane, unifies many branches of classical analysis and is necessary introduction to functional analysis. Professor Copson's book, which is based on lectures given to third-year undergraduates at the University of St Andrews, provides a more leisurely treatment of metric spaces than is found in books on functional analysis, which are usually written at graduate student level. His presentation is aimed at the applications of the theory to classical algebra and analysis; in particular, the chapter on contraction mappings shows how it provides proof of many of the existence theorems in classical analysis.

Genres: Mathematics

152 pages, Hardcover

First published May 1, 1968

Reviews

[Matt · Rating 4 out of 5]

Having been introduced to metric spaces in a couple of books in real analysis (Steven Lay's and William Trench's), this was a great supplementary text to have, particularly with all the applications the author brings out in his lectures including his emphases on the links to functional analysis and general topology, as well as more applied fields like Fourier series, fixed point and contraction mapping theorems, and numerical methods for solving systems of equations and differential equations.

The downside is that much is presumed by the author including the reader's understanding of complex analysis (something I have woefully neglected to getting around to), and little time is spent on any one topic, leading to a breathtakingly quick pace.

I'll definitely be keeping this one around for reference and occasionally reworking through the proofs as I start to encounter metric spaces and theorems pertaining to them in my grad courses in economics and game theory.

[Andrew Cavallo · Rating 5 out of 5]

Chapter eight, which is about applications with respect to analysis, is vast, large-scale.