Overview
- Authors:
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Alexander Arhangel’skii
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Ohio University, Athens, USA
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Mikhail Tkachenko
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Universidad Autónoma Metropolitana, Mexico City, Mexico
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Table of contents (10 chapters)
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- Alexander Arhangel’skii, Mikhail Tkachenko
Pages 1-89
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- Alexander Arhangel’skii, Mikhail Tkachenko
Pages 90-133
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- Alexander Arhangel’skii, Mikhail Tkachenko
Pages 134-215
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- Alexander Arhangel’skii, Mikhail Tkachenko
Pages 216-284
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- Alexander Arhangel’skii, Mikhail Tkachenko
Pages 285-344
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- Alexander Arhangel’skii, Mikhail Tkachenko
Pages 345-408
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- Alexander Arhangel’skii, Mikhail Tkachenko
Pages 409-514
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- Alexander Arhangel’skii, Mikhail Tkachenko
Pages 515-570
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- Alexander Arhangel’skii, Mikhail Tkachenko
Pages 571-696
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- Alexander Arhangel’skii, Mikhail Tkachenko
Pages 697-733
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Back Matter
Pages 735-781
About this book
Algebraandtopology,thetwofundamentaldomainsofmathematics,playcomplem- tary roles. Topology studies continuity and convergence and provides a general framework to study the concept of a limit. Much of topology is devoted to handling in?nite sets and in?nity itself; the methods developed are qualitative and, in a certain sense, irrational. - gebra studies all kinds of operations and provides a basis for algorithms and calculations. Very often, the methods here are ?nitistic in nature. Because of this difference in nature, algebra and topology have a strong tendency to develop independently, not in direct contact with each other. However, in applications, in higher level domains of mathematics, such as functional analysis, dynamical systems, representation theory, and others, topology and algebra come in contact most naturally. Many of the most important objects of mathematics represent a blend of algebraic and of topologicalstructures. Topologicalfunctionspacesandlineartopologicalspacesingeneral, topological groups and topological ?elds, transformation groups, topological lattices are objects of this kind. Very often an algebraic structure and a topology come naturally together; this is the case when they are both determined by the nature of the elements of the set considered (a group of transformations is a typical example). The rules that describe the relationship between a topology and an algebraic operation are almost always transparentandnatural—theoperationhastobecontinuous,jointlyorseparately.
Authors and Affiliations
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Ohio University, Athens, USA
Alexander Arhangel’skii
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Universidad Autónoma Metropolitana, Mexico City, Mexico
Mikhail Tkachenko
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