Introduction to Metric and Topological Spaces

Released on by Wilson A Sutherland
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  • Introduction to Metric and Topological Spaces Book Detail

  • Author : Wilson A Sutherland
  • Release Date : 2009-06-18
  • Publisher : Oxford University Press
  • Genre : Mathematics
  • Pages : 219
  • ISBN 13 : 0191568309
  • File Size : 26,26 MB
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Introduction to Metric and Topological Spaces by Wilson A Sutherland PDF Summary

Book Description: 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 of metric 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 convey familiarity. 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 Möbius 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 as the 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 by hints, as well as a companion website, with further explanations and examples as well as material supplementary to that in the book.

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Topology of Metric Spaces

Topology of Metric Spaces

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"Topology of Metric Spaces gives a very streamlined development of a course in metric space topology emphasizing only the most useful concepts, concrete spaces

Topological Spaces

Topological Spaces

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gentle introduction to the subject, leading the reader to understand the notion of what is important in topology with regard to geometry. Divided into three sec