On compact weaker topologies in function spaces

In this paper we prove that for every cardinal kappa, the space C-p(D-k) admits a continuous bijection onto a space whose all finite powers are Lindelof (the symbol D stands for the discrete two-point space). We also prove that for every metrizable compact space X, the space Cp (X) can be condensed...

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Detalhes bibliográficos
Autor: Casarrubias-Segura, F
Tipo de documento: artigo
Estado:Versão publicada
Data de publicação:2001
País:México
Recursos:Universidad Nacional Autónoma de México
Repositório:Sistema de Información de la Facultad de Ciencias, UNAM
OAI Identifier:oai:repositorio.fciencias.unam.mx:11154/1946
Acesso em linha:http://hdl.handle.net/11154/1946
Access Level:Acceso aberto
Palavra-chave:Mathematics, Applied
Mathematics
function spaces
condensation
topology of pointwise convergence
weaker topologies
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spelling On compact weaker topologies in function spacesCasarrubias-Segura, FMathematics, AppliedMathematicsfunction spacescondensationtopology of pointwise convergenceweaker topologiesIn this paper we prove that for every cardinal kappa, the space C-p(D-k) admits a continuous bijection onto a space whose all finite powers are Lindelof (the symbol D stands for the discrete two-point space). We also prove that for every metrizable compact space X, the space Cp (X) can be condensed (i.e., admits a continuous bijection) onto the Hilbert cube I-omega. As a consequence it is established that the space Cp (DI) can be condensed onto a compact space. In connection to this result, we also prove that there exist models of ZFC in which the statement "The spaces C-p(D-k) can be condensed onto a compact space for every cardinal kappa > omega" is not true. We show also that for every cardinal K, the spaces C-p(C-p(D-k)) and L-p(D-k) have dense subsets of countable tightness. (C) 2001 Elsevier Science B.V. All rights reserved.2011-01-22T10:26:57Z2011-01-22T10:26:57Z2001info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article0166-8641http://hdl.handle.net/11154/19462316115(3):291-298reponame:Sistema de Información de la Facultad de Ciencias, UNAMinstname:Universidad Nacional Autónoma de Méxicoinstacron:UNAMenTopology and Its Applicationsinfo:eu-repo/semantics/openAccessoai:repositorio.fciencias.unam.mx:11154/19462025-09-17T19:20:38Z
dc.title.none.fl_str_mv On compact weaker topologies in function spaces
title On compact weaker topologies in function spaces
spellingShingle On compact weaker topologies in function spaces
Casarrubias-Segura, F
Mathematics, Applied
Mathematics
function spaces
condensation
topology of pointwise convergence
weaker topologies
title_short On compact weaker topologies in function spaces
title_full On compact weaker topologies in function spaces
title_fullStr On compact weaker topologies in function spaces
title_full_unstemmed On compact weaker topologies in function spaces
title_sort On compact weaker topologies in function spaces
dc.creator.none.fl_str_mv Casarrubias-Segura, F
author Casarrubias-Segura, F
author_facet Casarrubias-Segura, F
author_role author
dc.subject.none.fl_str_mv Mathematics, Applied
Mathematics
function spaces
condensation
topology of pointwise convergence
weaker topologies
topic Mathematics, Applied
Mathematics
function spaces
condensation
topology of pointwise convergence
weaker topologies
description In this paper we prove that for every cardinal kappa, the space C-p(D-k) admits a continuous bijection onto a space whose all finite powers are Lindelof (the symbol D stands for the discrete two-point space). We also prove that for every metrizable compact space X, the space Cp (X) can be condensed (i.e., admits a continuous bijection) onto the Hilbert cube I-omega. As a consequence it is established that the space Cp (DI) can be condensed onto a compact space. In connection to this result, we also prove that there exist models of ZFC in which the statement "The spaces C-p(D-k) can be condensed onto a compact space for every cardinal kappa > omega" is not true. We show also that for every cardinal K, the spaces C-p(C-p(D-k)) and L-p(D-k) have dense subsets of countable tightness. (C) 2001 Elsevier Science B.V. All rights reserved.
publishDate 2001
dc.date.none.fl_str_mv 2001
2011-01-22T10:26:57Z
2011-01-22T10:26:57Z
dc.type.none.fl_str_mv info:eu-repo/semantics/publishedVersion
info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv 0166-8641
http://hdl.handle.net/11154/1946
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identifier_str_mv 0166-8641
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url http://hdl.handle.net/11154/1946
dc.language.none.fl_str_mv en
language_invalid_str_mv en
dc.relation.none.fl_str_mv Topology and Its Applications
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.source.none.fl_str_mv 115(3):291-298
reponame:Sistema de Información de la Facultad de Ciencias, UNAM
instname:Universidad Nacional Autónoma de México
instacron:UNAM
instname_str Universidad Nacional Autónoma de México
instacron_str UNAM
institution UNAM
reponame_str Sistema de Información de la Facultad de Ciencias, UNAM
collection Sistema de Información de la Facultad de Ciencias, UNAM
repository.name.fl_str_mv
repository.mail.fl_str_mv
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