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＜電子ブック＞
Topological Groups and Related Structures, An Introduction to Topological Algebra / by Alexander Arhangel’skii, Mikhail Tkachenko
(Atlantis Studies in Mathematics. ISSN:22151885 ; 1)

版	1st ed. 2008.
出版者	(Paris : Atlantis Press : Imprint: Atlantis Press)
出版年	2008
大きさ	XIV, 781 p : online resource
著者標目	*Arhangel’skii, Alexander author Tkachenko, Mikhail author SpringerLink (Online service)
件　名	LCSH:Group theory LCSH:Algebraic topology FREE:Group Theory and Generalizations FREE:Algebraic Topology
一般注記	to Topological Groups and Semigroups -- Right Topological and Semitopological Groups -- Topological groups: Basic constructions -- Some Special Classes of Topological Groups -- Cardinal Invariants of Topological Groups -- Moscow Topological Groups and Completions of Groups -- Free Topological Groups -- R-Factorizable Topological Groups -- Compactness and its Generalizations in Topological Groups -- Actions of Topological Groups on Topological Spaces 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 HTTP:URL=https://doi.org/10.2991/978-94-91216-35-0

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