Metric Spaces /
Shirali, Satish.
Metric Spaces / by Satish Shirali, Harkrishan L. Vasudeva. - viii, 222 páginas 21 ilustraciones recurso en línea.
Springer eBooks
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.
9781846282447
10.1007/1846282446 doi
QA319-329.9
Metric Spaces / by Satish Shirali, Harkrishan L. Vasudeva. - viii, 222 páginas 21 ilustraciones recurso en línea.
Springer eBooks
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.
9781846282447
10.1007/1846282446 doi
QA319-329.9