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An Dr Mícheál Ó Searcóid

Metric Spaces



Springer-Verlag, August 2006


This book is truly about metric spaces. ... The book is packed full of material which does not often appear in comparable books. ... His use of questions to increase understanding and to move on to the next topic are also to be appreciated. ... this is a great book and suitable ... for third-and fourth-year under-graduates and beginning graduate students.

Marion Cohen, MathDL, January, 2007


This book provides a wonderful introduction to metric spaces, highly suitable for self-study. The pace is very leisurely, including a great many examples (so many that I skipped quite a few of them) and complete proofs. (More mathematically mature readers might find the pace too slow.) The coverage is quite thorough with individual chapters devoted to key topics such as convergence, continuity, completeness, compactness and metric equivalence. Solutions to various problems are included. Prerequisites are calculus and elementary real analysis.

gengogakusha, Tarrytown, NY USA, Amazon.com


The book is very readable. It includes appendixes on the necessary mathematical logic and set theory, and has a substantial number of exercises ... Every concept is demonstrated via a large number of examples, starting with commonplace ones and expanding the reader's horizon with the more abstruse ones, to give a sense of the scope of the concepts ... A useful addition to any library supporting an undergraduate mathematics major.

D. Z. Spicer, CHOICE, March 2007


... this book focuses on metric spaces as an object of investigation interesting on its own ... [it] is a very polished book written in a style similar to Bourbaki's. It has a reference chart, showing the dependencies on a section-by-section basis as well as two appendices on Language and Logic and on Sets. Moreover, it contains solutions to many of its exercises.

H. Brandenburg, Zentralblatt MATH


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