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Metric Spaces
English
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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.
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