Pointwise convergence and Ascoli theorems for nearness spaces

[EN] We first study subspaces and product spaces in the context of nearness spaces and prove that U-N spaces, C-N spaces, PN spaces and totally bounded nearness spaces are nearness hereditary; T-N spaces and compact nearness spaces are N-closed hereditary. We prove that N2 plus compact implies N-clo...

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Detalles Bibliográficos
Autor: Yang, Zhanbo
Tipo de recurso: artículo
Fecha de publicación:2009
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/86550
Acceso en línea:https://riunet.upv.es/handle/10251/86550
Access Level:acceso abierto
Palabra clave:Nearness spaces
Subspace
Product space
Neighborhood system
Pointwise convergent
Ascoli’s theorem
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spelling Pointwise convergence and Ascoli theorems for nearness spacesYang, ZhanboNearness spacesSubspaceProduct spaceNeighborhood systemPointwise convergentAscoli’s theorem[EN] We first study subspaces and product spaces in the context of nearness spaces and prove that U-N spaces, C-N spaces, PN spaces and totally bounded nearness spaces are nearness hereditary; T-N spaces and compact nearness spaces are N-closed hereditary. We prove that N2 plus compact implies N-closed subsets. We prove that totally bounded, compact and N2 are productive. We generalize the concepts of neighborhood systems into the nearness spaces and prove that the nearness neighborhood systems are consistent with existing concepts of neighborhood systems in topological spaces, uniform spaces and proximity spaces respectively when considered in the respective sub-categories. We prove that a net of functions is convergent under the pointwise convergent nearness structure if and only if its cross-section at each point is convergent. We have also proved two Ascoli-Arzelà type of theorems.This work was in part supported by a grant from the 2008 Faculty Research Fund of the University of the Incarnate Word.Universitat Politècnica de ValènciaUniversity of the Incarnate Word, EEUURepositorio Institucional de la Universitat Politècnica de València Riunet20092009-04-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/86550reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) http://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/865502026-06-13T07:49:27Z
dc.title.none.fl_str_mv Pointwise convergence and Ascoli theorems for nearness spaces
title Pointwise convergence and Ascoli theorems for nearness spaces
spellingShingle Pointwise convergence and Ascoli theorems for nearness spaces
Yang, Zhanbo
Nearness spaces
Subspace
Product space
Neighborhood system
Pointwise convergent
Ascoli’s theorem
title_short Pointwise convergence and Ascoli theorems for nearness spaces
title_full Pointwise convergence and Ascoli theorems for nearness spaces
title_fullStr Pointwise convergence and Ascoli theorems for nearness spaces
title_full_unstemmed Pointwise convergence and Ascoli theorems for nearness spaces
title_sort Pointwise convergence and Ascoli theorems for nearness spaces
dc.creator.none.fl_str_mv Yang, Zhanbo
author Yang, Zhanbo
author_facet Yang, Zhanbo
author_role author
dc.contributor.none.fl_str_mv University of the Incarnate Word, EEUU
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Nearness spaces
Subspace
Product space
Neighborhood system
Pointwise convergent
Ascoli’s theorem
topic Nearness spaces
Subspace
Product space
Neighborhood system
Pointwise convergent
Ascoli’s theorem
description [EN] We first study subspaces and product spaces in the context of nearness spaces and prove that U-N spaces, C-N spaces, PN spaces and totally bounded nearness spaces are nearness hereditary; T-N spaces and compact nearness spaces are N-closed hereditary. We prove that N2 plus compact implies N-closed subsets. We prove that totally bounded, compact and N2 are productive. We generalize the concepts of neighborhood systems into the nearness spaces and prove that the nearness neighborhood systems are consistent with existing concepts of neighborhood systems in topological spaces, uniform spaces and proximity spaces respectively when considered in the respective sub-categories. We prove that a net of functions is convergent under the pointwise convergent nearness structure if and only if its cross-section at each point is convergent. We have also proved two Ascoli-Arzelà type of theorems.
publishDate 2009
dc.date.none.fl_str_mv 2009
2009-04-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/86550
url https://riunet.upv.es/handle/10251/86550
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
Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
http://creativecommons.org/licenses/by-nc-nd/4.0/
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
Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Universitat Politècnica de València
publisher.none.fl_str_mv Universitat Politècnica de València
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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