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Metric Spaces

By: Shirali, Satish [author.].
Contributor(s): Vasudeva, Harkrishan L [author.] | SpringerLink (Online service).
Material type: materialTypeLabelBookPublisher: London : Springer London, 2006.Description: VIII, 222 p. 21 illus. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9781846282447.Subject(s): Mathematics | Functional analysis | Topology | Physics | Engineering | Mathematics | Topology | Functional Analysis | Mathematical Methods in Physics | Engineering, generalDDC classification: 514 Online resources: Click here to access online
Contents:
Preliminaries -- Basic Concepts -- Topology of a Metric Space -- Continuity -- Connected Spaces -- Compact Spaces -- Product Spaces.
In: Springer eBooksSummary: 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.
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Preliminaries -- Basic Concepts -- Topology of a Metric Space -- Continuity -- Connected Spaces -- Compact Spaces -- Product Spaces.

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.

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