Introduction to Metric and Topological Spaces
Edition: 2nd 2009
List price: $40.95
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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 andtopological 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 therest 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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All the information you need in one place! Each Study Brief is a summary of one specific subject; facts, figures, and explanations to help you learn faster.
List price: $40.95
Copyright year: 2009
Publisher: Oxford University Press, Incorporated
Publication date: 10/4/2009
Size: 6.25" wide x 9.25" long x 0.75" tall
|Notation and terminology|
|More on sets and functions|
|Review of some real analysis|
|More concepts in metric spaces|
|Continuity in topological spaces bases|
|Some concepts in topological spaces|
|Subspaces and product spaces|
|The Hausdorff condition|
|Quotient spaces and surfaces|
|Complete metric spaces|