Springer Undergraduate Mathematics Series

Metric Spaces

Authors: O'Searcoid, Mícheál

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eBook $34.99
price for USA (gross)
  • ISBN 978-1-84628-627-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
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  • Immediate eBook download after purchase
Softcover $49.95
price for USA
  • ISBN 978-1-84628-369-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

The abstract concepts of metric ces are often perceived as difficult. This book offers a unique approach to the subject which gives readers the advantage of a new perspective familiar from the analysis of a real line. 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.

The book goes on to provide a thorough exposition of all the standard necessary results of the theory and, in addition, includes selected topics not normally found in introductory books, such as: the Tietze Extension Theorem; the Hausdorff metric and its completeness; and the existence of curves of minimum length. Other features include:

  • end-of-chapter summaries and numerous exercises to reinforce what has been learnt;
  • extensive cross-referencing to help the reader follow arguments;
  • a Cumulative Reference Chart, showing the dependencies throughout the book on a section-by-section basis as an aid to course design.

The book is designed for third- and fourth-year undergraduates and beginning graduates. Readers should have some practical knowledge of differential and integral calculus and have completed a first course in real analysis. 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.

About the authors

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).

Reviews

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)


Table of contents (10 chapters)

Buy this book

eBook $34.99
price for USA (gross)
  • ISBN 978-1-84628-627-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA
  • ISBN 978-1-84628-369-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Metric Spaces
Authors
Series Title
Springer Undergraduate Mathematics Series
Copyright
2007
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London
eBook ISBN
978-1-84628-627-8
DOI
10.1007/978-1-84628-627-8
Softcover ISBN
978-1-84628-369-7
Series ISSN
1615-2085
Edition Number
1
Number of Pages
XX, 304
Number of Illustrations and Tables
102 b/w illustrations
Topics