Atlantis Studies in Mathematics

Topological Groups and Related Structures, An Introduction to Topological Algebra.

Authors: Arhangel’skii, Alexander, Tkachenko, Mikhail

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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.

Table of contents (10 chapters)

  • Introduction to Topological Groups and Semigroups

    Arhangel’skii, Alexander (et al.)

    Pages 1-89

  • Right Topological and Semitopological Groups

    Arhangel’skii, Alexander (et al.)

    Pages 90-133

  • Topological groups: Basic constructions

    Arhangel’skii, Alexander (et al.)

    Pages 134-215

  • Some Special Classes of Topological Groups

    Arhangel’skii, Alexander (et al.)

    Pages 216-284

  • Cardinal Invariants of Topological Groups

    Arhangel’skii, Alexander (et al.)

    Pages 285-344

Buy this book

eBook $169.00
price for USA (gross)
  • ISBN 978-94-91216-35-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
Topological Groups and Related Structures, An Introduction to Topological Algebra.
Authors
Series Title
Atlantis Studies in Mathematics
Series Volume
1
Copyright
2008
Publisher
Atlantis Press
Copyright Holder
Atlantis Press and the authors
eBook ISBN
978-94-91216-35-0
DOI
10.2991/978-94-91216-35-0
Series ISSN
1875-7634
Edition Number
1
Number of Pages
XIV, 781
Topics