Metric Spaces

Mícheál Ó Searcóid is author of another, higher-level, SUMS book, Elements of Abstract Analysis, 1-85233-424-X, published November 2001, sales (as of June 2005): 1051 (ROW: 634; US: 417).

• Metrics.- Distance.- Boundary.- Open, Closed and Dense Subsets.- Balls.- Convergence.- Bounds.- Continuity.- Uniform Continuity.- Completeness.- Connectedness.- Compactness.- Equivalence.

From the reviews: "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) "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)