Topological automorphism groups of chains

It is shown that any set--open topology on the automorphism group $A(X)$ of a chain $X$ coincides with the pointwise topology and that $A(X)$ is a topological group with respect to this topology. Topological properties of connectedness and compactness in $A(X)$ are investigated. In particular, it is...

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Author: Ovchinnikov, Sergei V.
Format: article
Publication Date:2001
Country:España
Institution:Universitat Politècnica de Catalunya (UPC)
Repository:UPCommons. Portal del coneixement obert de la UPC
Language:English
OAI Identifier:oai:upcommons.upc.edu:2099/3592
Online Access:https://hdl.handle.net/2099/3592
Access Level:Open access
Keyword:Automorphism group
Function space
Robustness
Estructures algebraiques ordenades
Classificació AMS::06 Order, lattices, ordered algebraic structures::06F Ordered structures
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spelling Topological automorphism groups of chainsOvchinnikov, Sergei V.Automorphism groupFunction spaceRobustnessEstructures algebraiques ordenadesClassificació AMS::06 Order, lattices, ordered algebraic structures::06F Ordered structuresIt is shown that any set--open topology on the automorphism group $A(X)$ of a chain $X$ coincides with the pointwise topology and that $A(X)$ is a topological group with respect to this topology. Topological properties of connectedness and compactness in $A(X)$ are investigated. In particular, it is shown that the automorphism group of a doubly homogeneous chain is generated by any neighborhood of the identity element.Universitat Politècnica de Catalunya. Secció de Matemàtiques i Informàtica20012001-01-0120072007-09-28journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2099/3592reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2http://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2099/35922026-05-27T15:37:01Z
dc.title.none.fl_str_mv Topological automorphism groups of chains
title Topological automorphism groups of chains
spellingShingle Topological automorphism groups of chains
Ovchinnikov, Sergei V.
Automorphism group
Function space
Robustness
Estructures algebraiques ordenades
Classificació AMS::06 Order, lattices, ordered algebraic structures::06F Ordered structures
title_short Topological automorphism groups of chains
title_full Topological automorphism groups of chains
title_fullStr Topological automorphism groups of chains
title_full_unstemmed Topological automorphism groups of chains
title_sort Topological automorphism groups of chains
dc.creator.none.fl_str_mv Ovchinnikov, Sergei V.
author Ovchinnikov, Sergei V.
author_facet Ovchinnikov, Sergei V.
author_role author
dc.subject.none.fl_str_mv Automorphism group
Function space
Robustness
Estructures algebraiques ordenades
Classificació AMS::06 Order, lattices, ordered algebraic structures::06F Ordered structures
topic Automorphism group
Function space
Robustness
Estructures algebraiques ordenades
Classificació AMS::06 Order, lattices, ordered algebraic structures::06F Ordered structures
description It is shown that any set--open topology on the automorphism group $A(X)$ of a chain $X$ coincides with the pointwise topology and that $A(X)$ is a topological group with respect to this topology. Topological properties of connectedness and compactness in $A(X)$ are investigated. In particular, it is shown that the automorphism group of a doubly homogeneous chain is generated by any neighborhood of the identity element.
publishDate 2001
dc.date.none.fl_str_mv 2001
2001-01-01
2007
2007-09-28
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2099/3592
url https://hdl.handle.net/2099/3592
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2

http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2

http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Universitat Politècnica de Catalunya. Secció de Matemàtiques i Informàtica
publisher.none.fl_str_mv Universitat Politècnica de Catalunya. Secció de Matemàtiques i Informàtica
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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