Topological Groups and Related Structures

  • Alexander Arhangel’skii
  • Mikhail Tkachenko
Book

Part of the Atlantis Studies in Mathematics book series (ATLANTISSM, volume 1)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Alexander Arhangel’skii, Mikhail Tkachenko
    Pages 1-89
  3. Alexander Arhangel’skii, Mikhail Tkachenko
    Pages 90-133
  4. Alexander Arhangel’skii, Mikhail Tkachenko
    Pages 134-215
  5. Alexander Arhangel’skii, Mikhail Tkachenko
    Pages 216-284
  6. Alexander Arhangel’skii, Mikhail Tkachenko
    Pages 285-344
  7. Alexander Arhangel’skii, Mikhail Tkachenko
    Pages 345-408
  8. Alexander Arhangel’skii, Mikhail Tkachenko
    Pages 409-514
  9. Alexander Arhangel’skii, Mikhail Tkachenko
    Pages 515-570
  10. Alexander Arhangel’skii, Mikhail Tkachenko
    Pages 571-696
  11. Alexander Arhangel’skii, Mikhail Tkachenko
    Pages 697-733
  12. Back Matter
    Pages 735-781

About this book

Introduction

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.

Keywords

Area Scope algebra cardinal invariant cardinal invariants compactness construction eXist interface knowledge object semigroup set theory topological group topology

Authors and affiliations

  • Alexander Arhangel’skii
    • 1
  • Mikhail Tkachenko
    • 2
  1. 1.Ohio UniversityAthensUSA
  2. 2.Universidad Autónoma MetropolitanaMexico CityMexico

Bibliographic information

  • DOI https://doi.org/10.2991/978-94-91216-35-0
  • Copyright Information Atlantis Press and the authors 2008
  • Publisher Name Atlantis Press
  • eBook Packages Mathematics and Statistics
  • Online ISBN 978-94-91216-35-0
  • Series Print ISSN 1875-7634
  • About this book