I-Fréchet-Urysohn property in Cα(X)

[EN] In this paper, we introduce I-Fr´echet-Urysohn, strongly I-Fr´echet-Urysohn and strictly I-Fr´echet-Urysohn spaces,discuses their properties of countable tightness and mappings that preserve these spaces.Meanwhile, we discuss the internal characterizations of these spaces in C?(X).The following...

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Bibliographic Details
Author: Zhou, Xiangeng
Format: article
Publication Date:2026
Country:España
Institution:Universitat Politècnica de València (UPV)
Repository:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Language:English
OAI Identifier:oai:dnet:riunet______::a7f27194bbbc30672d5f9041cbe232dc
Online Access:https://riunet.upv.es/handle/10251/233563
Access Level:Open access
Keyword:I-Fréchet-Urysohn spaces
strongly I-Fréchet-Urysohn spaces
strictly IFréchet-Urysohn spaces
Countable tightness
Set-open topology
Functional spaces
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network_acronym_str ES
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spelling I-Fréchet-Urysohn property in Cα(X)Zhou, XiangengI-Fréchet-Urysohn spacesstrongly I-Fréchet-Urysohn spacesstrictly IFréchet-Urysohn spacesCountable tightnessSet-open topologyFunctional spaces[EN] In this paper, we introduce I-Fr´echet-Urysohn, strongly I-Fr´echet-Urysohn and strictly I-Fr´echet-Urysohn spaces,discuses their properties of countable tightness and mappings that preserve these spaces.Meanwhile, we discuss the internal characterizations of these spaces in C?(X).The following main theorem is obtained. Theorem. Let ? be a network of X. The following are equivalent. (1) Cα(X) is a strictly I-Fr´echet-Urysohn space. (2) Cα(X) is a strongly I-Fr´echet-Urysohn space. (3) Cα(X) is an I-Fr´echet-Urysohn space. (4) Every open α-cover of X contains an I-α-sequence. (5) If {Un}n∈N is a sequence of open α-cover of X, then there is an I-α-sequence {un}n∈N of X such that each un ∈ Un. (6) Cωα (X) is a strictly I-Fréchet-Urysohn space.Universitat Politècnica de ValènciaNational Natural Science Foundation of ChinaNatural Science Foundation of Fujian ProvinceRepositorio Institucional de la Universitat Politècnica de València Riunet20262026-03-16journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/233563reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengNational Natural Science Foundation of China https://doi.org/10.13039/501100001809 GeneralProgram 12171015NaturalScienceFoundationOfFujianProvince NaturalScienceFoundationOfFujianProvince ResearchProject 2023J011078NaturalScienceFoundationOfFujianProvince NaturalScienceFoundationOfFujianProvince ResearchProject 2024J01933open accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento - No comercial - Compartir igual (by-nc-sa) http://creativecommons.org/licenses/by-nc-sa/4.0/info:eu-repo/semantics/openAccessoai:dnet:riunet______::a7f27194bbbc30672d5f9041cbe232dc2026-06-13T07:49:27Z
dc.title.none.fl_str_mv I-Fréchet-Urysohn property in Cα(X)
title I-Fréchet-Urysohn property in Cα(X)
spellingShingle I-Fréchet-Urysohn property in Cα(X)
Zhou, Xiangeng
I-Fréchet-Urysohn spaces
strongly I-Fréchet-Urysohn spaces
strictly IFréchet-Urysohn spaces
Countable tightness
Set-open topology
Functional spaces
title_short I-Fréchet-Urysohn property in Cα(X)
title_full I-Fréchet-Urysohn property in Cα(X)
title_fullStr I-Fréchet-Urysohn property in Cα(X)
title_full_unstemmed I-Fréchet-Urysohn property in Cα(X)
title_sort I-Fréchet-Urysohn property in Cα(X)
dc.creator.none.fl_str_mv Zhou, Xiangeng
author Zhou, Xiangeng
author_facet Zhou, Xiangeng
author_role author
dc.contributor.none.fl_str_mv National Natural Science Foundation of China
Natural Science Foundation of Fujian Province
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv I-Fréchet-Urysohn spaces
strongly I-Fréchet-Urysohn spaces
strictly IFréchet-Urysohn spaces
Countable tightness
Set-open topology
Functional spaces
topic I-Fréchet-Urysohn spaces
strongly I-Fréchet-Urysohn spaces
strictly IFréchet-Urysohn spaces
Countable tightness
Set-open topology
Functional spaces
description [EN] In this paper, we introduce I-Fr´echet-Urysohn, strongly I-Fr´echet-Urysohn and strictly I-Fr´echet-Urysohn spaces,discuses their properties of countable tightness and mappings that preserve these spaces.Meanwhile, we discuss the internal characterizations of these spaces in C?(X).The following main theorem is obtained. Theorem. Let ? be a network of X. The following are equivalent. (1) Cα(X) is a strictly I-Fr´echet-Urysohn space. (2) Cα(X) is a strongly I-Fr´echet-Urysohn space. (3) Cα(X) is an I-Fr´echet-Urysohn space. (4) Every open α-cover of X contains an I-α-sequence. (5) If {Un}n∈N is a sequence of open α-cover of X, then there is an I-α-sequence {un}n∈N of X such that each un ∈ Un. (6) Cωα (X) is a strictly I-Fréchet-Urysohn space.
publishDate 2026
dc.date.none.fl_str_mv 2026
2026-03-16
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/10251/233563
url https://riunet.upv.es/handle/10251/233563
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv National Natural Science Foundation of China https://doi.org/10.13039/501100001809 GeneralProgram 12171015
NaturalScienceFoundationOfFujianProvince NaturalScienceFoundationOfFujianProvince ResearchProject 2023J011078
NaturalScienceFoundationOfFujianProvince NaturalScienceFoundationOfFujianProvince ResearchProject 2024J01933
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento - No comercial - Compartir igual (by-nc-sa)
http://creativecommons.org/licenses/by-nc-sa/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 - Compartir igual (by-nc-sa)
http://creativecommons.org/licenses/by-nc-sa/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 15,812429

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