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Metric Spaces with 21 Figures

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ISBN: 9781447174257
Table of Content Sample Pages

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.

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Product Description

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    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.
Additional Information
    Publisher Springer
    Binding Paperback
    Year 2023
    Edition 1st Edition
    Pages 230
    Author S. Shirali
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