The abstract concepts of metric spaces are often perceived as difficult. This book offers a unique approach to the subject which gives readers the advantage of a new perspective on ideas familiar from the analysis of a real line. With its many examples, careful illustrations, and full solutions to selected exercises, this book provides a gentle introduction that is ideal for self-study and an excellent preparation for applications.

Each chapter features copious examples and numerous problems with solutions to some of these provided at the back of the book. Rather than passing quickly from the definition of a metric to the more abstract concepts of convergence and continuity, the author takes the concrete notion of distance as far as possible, illustrating the text with examples and naturally arising questions. Attention to detail at this stage is designed to prepare the reader to understand the more abstract ideas with relative ease.

Autorentext

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).

Inhalt

To the Reader.- Cumulative Reference Chart.- Metrics.- Distance.- Boundary.- Open, Closed and Dense Sets.- Balls.- Convergence.- Bounds.- Continuity.- Uniform Continuity.- Completeness.- Connectedness.- Compactness.- Equivalence.- Appendices: Language and Logic.- Sets.- Solutions.- List of Symbols.- Index.