Topological groups: local versus global

It is well known that locally compact groups are paracompact. We observe that this theorem can be generalized as follows: every locally paracompact group is paracompact. We prove a more general version of this statement using quotients. Similar ‘local implies global’ theorems hold also for many othe...

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Bibliographic Details
Main Authors:	A.V. Arhangelskii, Vladimir V. Uspenskij
Format:	Article
Language:	English
Published:	Universitat Politècnica de València 2006-04-01
Series:	Applied General Topology
Subjects:	Topological group Paracompact Lindelöf Local properties
Online Access:	http://polipapers.upv.es/index.php/AGT/article/view/1933

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spelling	doaj-890c4aa826504547b8eb471391861db22020-11-25T00:01:33ZengUniversitat Politècnica de ValènciaApplied General Topology1576-94021989-41472006-04-0171677210.4995/agt.2006.19331558Topological groups: local versus globalA.V. Arhangelskii0Vladimir V. Uspenskij1Ohio UniversityOhio UniversityIt is well known that locally compact groups are paracompact. We observe that this theorem can be generalized as follows: every locally paracompact group is paracompact. We prove a more general version of this statement using quotients. Similar ‘local implies global’ theorems hold also for many other properties, such as normality, metacompactness, stratifiability, etc.http://polipapers.upv.es/index.php/AGT/article/view/1933Topological groupParacompactLindelöfLocal properties
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	A.V. Arhangelskii Vladimir V. Uspenskij
spellingShingle	A.V. Arhangelskii Vladimir V. Uspenskij Topological groups: local versus global Applied General Topology Topological group Paracompact Lindelöf Local properties
author_facet	A.V. Arhangelskii Vladimir V. Uspenskij
author_sort	A.V. Arhangelskii
title	Topological groups: local versus global
title_short	Topological groups: local versus global
title_full	Topological groups: local versus global
title_fullStr	Topological groups: local versus global
title_full_unstemmed	Topological groups: local versus global
title_sort	topological groups: local versus global
publisher	Universitat Politècnica de València
series	Applied General Topology
issn	1576-9402 1989-4147
publishDate	2006-04-01
description	It is well known that locally compact groups are paracompact. We observe that this theorem can be generalized as follows: every locally paracompact group is paracompact. We prove a more general version of this statement using quotients. Similar ‘local implies global’ theorems hold also for many other properties, such as normality, metacompactness, stratifiability, etc.
topic	Topological group Paracompact Lindelöf Local properties
url	http://polipapers.upv.es/index.php/AGT/article/view/1933
work_keys_str_mv	AT avarhangelskii topologicalgroupslocalversusglobal AT vladimirvuspenskij topologicalgroupslocalversusglobal
_version_	1725441434875592704

Topological groups: local versus global

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