Metric Spaces (9781848008274)

This volume provides a complete introduction to metric space theory for undergraduates. It covers the topology of metric spaces, continuity, connectedness, compactness and product spaces, and includes results such as the Tietze-Urysohn extension theorem, Picard's theorem on ordinary differential equations, and the set of discontinuities of the pointwise limit of a sequence of continuous functions. Key features include: a full chapter on product metric spaces, including a proof of Tychonoff's Theorem a wealth of examples and counter-examples from real analysis, sequence spaces and spaces of continuous functions numerous exercises - with solutions to most of them - to test understanding. The only prerequisite is a familiarity with the basics of real analysis: the authors take care to ensure that no prior knowledge of measure theory, Banach spaces or Hilbert spaces is assumed. The material is developed at a leisurely pace and applications of the theory are discussed throughout, making this book ideal as a classroom text for third- and fourth-year undergraduates or as a self-study resource for graduate students and researchers.

Product details

• Format Paperback | 232 pages
• Dimensions 190 x 240 x 10mm | 404g
• Publication date 30 Aug 2008
• Publisher Springer
• Publication City/Country United States
• Language English
• ISBN10 1848008279
• ISBN13 9781848008274

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