000 03489nam a22004575i 4500
001 978-94-91216-35-0
003 DE-He213
005 20161121231218.0
007 cr nn 008mamaa
008 120301s2008 fr | s |||| 0|eng d
020 _a9789491216350
_9978-94-91216-35-0
024 7 _a10.2991/978-94-91216-35-0
_2doi
050 4 _aQA174-183
072 7 _aPBG
_2bicssc
072 7 _aMAT002010
_2bisacsh
082 0 4 _a512.2
_223
100 1 _aArhangel’skii, Alexander.
_eauthor.
245 1 0 _aTopological Groups and Related Structures
_h[electronic resource] /
_cby Alexander Arhangel’skii, Mikhail Tkachenko.
264 1 _aParis :
_bAtlantis Press,
_c2008.
300 _aXIV, 781p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aAtlantis Studies in Mathematics,
_x1875-7634 ;
_v1
505 0 _ato 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.
520 _aAlgebraandtopology,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.
650 0 _aMathematics.
650 0 _aGroup theory.
650 0 _aAlgebraic topology.
650 1 4 _aMathematics.
650 2 4 _aGroup Theory and Generalizations.
650 2 4 _aAlgebraic Topology.
700 1 _aTkachenko, Mikhail.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
830 0 _aAtlantis Studies in Mathematics,
_x1875-7634 ;
_v1
856 4 0 _uhttp://dx.doi.org/10.2991/978-94-91216-35-0
912 _aZDB-2-SMA
950 _aMathematics and Statistics (Springer-11649)
999 _c510206
_d510206