Introduction to Metric and Topological Spaces (Paperback)

Wilson A. Sutherland

ISBN 10: 019956308X / ISBN 13: 9780199563081

Verlag: Oxford University Press, Oxford, 2009

Beschreibung

Paperback. One of the ways in which topology has influenced other branches of mathematics in the past few decades is by putting the study of continuity and convergence into a general setting. This new edition of Wilson Sutherland's classic text introduces metric and topological spaces by describing some of that influence. The aim is to move gradually from familiar real analysis to abstract topological spaces, using metric spaces as a bridge between the two. The language ofmetric and topological spaces is established with continuity as the motivating concept. Several concepts are introduced, first in metric spaces and then repeated for topological spaces, to help conveyfamiliarity. The discussion develops to cover connectedness, compactness and completeness, a trio widely used in the rest of mathematics. Topology also has a more geometric aspect which is familiar in popular expositions of the subject as `rubber-sheet geometry', with pictures of Moebius bands, doughnuts, Klein bottles and the like; this geometric aspect is illustrated by describing some standard surfaces, and it is shown how all this fits into the same story asthe more analytic developments. The book is primarily aimed at second- or third-year mathematics students. There are numerous exercises, many of the more challenging ones accompanied byhints, as well as a companion website, with further explanations and examples as well as material supplementary to that in the book. This fully updated new edition of Wilson Sutherland's classic text, Introduction to Metric and Topological Spaces, establishes the language of metric and topological spaces with continuity as the motivating concept, before developing its discussion to cover compactness, connectedness, and completeness. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability. Bestandsnummer des Verkäufers 9780199563081

Bibliografische Details

Titel: Introduction to Metric and Topological ...

Verlag: Oxford University Press, Oxford

Erscheinungsdatum: 2009

Einband: Paperback

Zustand: new

Auflage: 2. Auflage

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The presentation, description and explanation throughout the seventeen short chapters are excellent, and the text can be described as self-contained, with many suitably chosen examples and exercises ,.. An interesting innovation for the new edition is having a companion web site in which more useful and relevant materials can be found. (Peter Shiu, The Mathematical Gazette)