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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Real analysis
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Introduction to Metric and Topological Spaces (Hardcover, 2nd Revised edition)
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Introduction to Metric and Topological Spaces (Hardcover, 2nd Revised edition)
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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 Mobius 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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