The topological structure of (homogeneous) spaces and groups with countable cs∗-character

In this paper we introduce and study three new cardinal topological invariants called the cs∗-, cs-, and sb-characters. The class of topological spaces with countable cs∗-character is closed under many topological operations and contains all N-spaces and all spaces with point-countable cs∗-network....

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Main Authors:	Taras Banak, Lubomyr Zdomskyi
Format:	Article
Language:	English
Published:	Universitat Politècnica de València 2004-04-01
Series:	Applied General Topology
Subjects:	sb-network cs-networ , cs∗-network Sequential topological group kω-group Topologically homogeneous space Small cardinal Cardinal invariant
Online Access:	http://polipapers.upv.es/index.php/AGT/article/view/1993

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spelling	doaj-7ee96f7213a14cffa41fdfdbbe4d351e2020-11-24T22:17:45ZengUniversitat Politècnica de ValènciaApplied General Topology1576-94021989-41472004-04-0151254810.4995/agt.2004.19931615The topological structure of (homogeneous) spaces and groups with countable cs∗-characterTaras Banak0Lubomyr Zdomskyi1Akademia SwietorzyskaIvan Franko Lviv National UniversityIn this paper we introduce and study three new cardinal topological invariants called the cs∗-, cs-, and sb-characters. The class of topological spaces with countable cs∗-character is closed under many topological operations and contains all N-spaces and all spaces with point-countable cs∗-network. Our principal result states that each non-metrizable sequential topological group with countable cs∗- character has countable pseudo-character and contains an open kω- subgroup. This result is specific for topological groups: under Martin Axiom there exists a sequential topologically homogeneous kω-space X with N0 = cs∗x (X) <ψ (X).http://polipapers.upv.es/index.php/AGT/article/view/1993sb-networkcs-networ, cs∗-networkSequential topological groupkω-groupTopologically homogeneous spaceSmall cardinalCardinal invariant
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Taras Banak Lubomyr Zdomskyi
spellingShingle	Taras Banak Lubomyr Zdomskyi The topological structure of (homogeneous) spaces and groups with countable cs∗-character Applied General Topology sb-network cs-networ , cs∗-network Sequential topological group kω-group Topologically homogeneous space Small cardinal Cardinal invariant
author_facet	Taras Banak Lubomyr Zdomskyi
author_sort	Taras Banak
title	The topological structure of (homogeneous) spaces and groups with countable cs∗-character
title_short	The topological structure of (homogeneous) spaces and groups with countable cs∗-character
title_full	The topological structure of (homogeneous) spaces and groups with countable cs∗-character
title_fullStr	The topological structure of (homogeneous) spaces and groups with countable cs∗-character
title_full_unstemmed	The topological structure of (homogeneous) spaces and groups with countable cs∗-character
title_sort	topological structure of (homogeneous) spaces and groups with countable cs∗-character
publisher	Universitat Politècnica de València
series	Applied General Topology
issn	1576-9402 1989-4147
publishDate	2004-04-01
description	In this paper we introduce and study three new cardinal topological invariants called the cs∗-, cs-, and sb-characters. The class of topological spaces with countable cs∗-character is closed under many topological operations and contains all N-spaces and all spaces with point-countable cs∗-network. Our principal result states that each non-metrizable sequential topological group with countable cs∗- character has countable pseudo-character and contains an open kω- subgroup. This result is specific for topological groups: under Martin Axiom there exists a sequential topologically homogeneous kω-space X with N0 = cs∗x (X) <ψ (X).
topic	sb-network cs-networ , cs∗-network Sequential topological group kω-group Topologically homogeneous space Small cardinal Cardinal invariant
url	http://polipapers.upv.es/index.php/AGT/article/view/1993
work_keys_str_mv	AT tarasbanak thetopologicalstructureofhomogeneousspacesandgroupswithcountablecscharacter AT lubomyrzdomskyi thetopologicalstructureofhomogeneousspacesandgroupswithcountablecscharacter AT tarasbanak topologicalstructureofhomogeneousspacesandgroupswithcountablecscharacter AT lubomyrzdomskyi topologicalstructureofhomogeneousspacesandgroupswithcountablecscharacter
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The topological structure of (homogeneous) spaces and groups with countable cs∗-character

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