Set-open topologies on function spaces

Let X and Y be topological spaces, F(X,Y) the set of all functions from X into Y and C(X,Y) the set of all continuous functions in F(X,Y). We study various set-open topologies tλ (λ ⊆ P(X)) on F(X,Y) and consider their existence, comparison and coincidence in the setting of Y a general topological s...

Full description

Saved in:
Bibliographic Details
Published in:Applied general topology Vol. 19; no. 1; pp. 55 - 64
Main Authors: Alqurashi, Wafa Khalaf, Khan, Liaqat Ali, Osipov, Alexander V.
Format: Journal Article
Language:English
Published: Universitat Politècnica de València 01.01.2018
Subjects:
C-compact- open topology
pseudocompact-open topology
quasi-uniform convergence topology
right K- completeness
set-open topology
α-continuous function
ISSN:1576-9402, 1989-4147
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract Let X and Y be topological spaces, F(X,Y) the set of all functions from X into Y and C(X,Y) the set of all continuous functions in F(X,Y). We study various set-open topologies tλ (λ ⊆ P(X)) on F(X,Y) and consider their existence, comparison and coincidence in the setting of Y a general topological space as well as for Y = R. Further, we consider the parallel notion of quasi-uniform convergence topologies Uλ (λ ⊆ P(X)) on F(X,Y) to discuss Uλ-closedness and right Uλ-K-completeness properties of a certain subspace of F(X,Y) in the case of Y a locally symmetric quasi-uniform space. We include some counter-examples to justify our comments.
AbstractList Let X and Y be topological spaces, F(X,Y) the set of all functions from X into Y and C(X,Y) the set of all continuous functions in F(X,Y). We study various set-open topologies tλ (λ ⊆ P(X)) on F(X,Y) and consider their existence, comparison and coincidence in the setting of Y a general topological space as well as for Y = R. Further, we consider the parallel notion of quasi-uniform convergence topologies Uλ (λ ⊆ P(X)) on F(X,Y) to discuss Uλ-closedness and right Uλ-K-completeness properties of a certain subspace of F(X,Y) in the case of Y a locally symmetric quasi-uniform space. We include some counter-examples to justify our comments.
Author Alqurashi, Wafa Khalaf
Khan, Liaqat Ali
Osipov, Alexander V.
Author_xml – sequence: 1
  givenname: Wafa Khalaf
  surname: Alqurashi
  fullname: Alqurashi, Wafa Khalaf
– sequence: 2
  givenname: Liaqat Ali
  orcidid: 0000-0002-0263-7270
  surname: Khan
  fullname: Khan, Liaqat Ali
– sequence: 3
  givenname: Alexander V.
  surname: Osipov
  fullname: Osipov, Alexander V.
BookMark eNptkD1PwzAQhi1UJErpyN6JLcWOz18jqvioVIkBmC3bsaNUIY5iM_DvcSgsiFvudLr3vbvnEi2GOHiErgneglLs1rR5W2Mit4JTfIaWRElVAQGxKDUTvFKA6wu0TumIS1DFgcIS3bz4XMXRD5scx9jHtvNpE4dN-Bhc7kqRRuN8ukLnwfTJr3_yCr093L_unqrD8-N-d3eoHIU6V0B9bcFRybwL0siGSCucwJZ43gjHbVNWiwBArW2YMZJyYgQI5oQDHBxdof3Jt4nmqMepezfTp46m09-NOLXaTLlzvdcuqEYB4aamFpgCq4S3jZcsAK25VMWLnrzcFFOafNCuy2Z-Kk-m6zXBeianCzk9k9MzuaKq_qh-r_h__gs2YnFK
CitedBy_id crossref_primary_10_1016_j_topol_2023_108523
Cites_doi 10.1016/j.topol.2014.10.008
10.1007/BF01961309
10.2307/1969088
10.1016/j.topol.2011.11.049
10.7146/math.scand.a-11072
10.1007/s10958-007-0258-3
10.1515/dema-2013-0413
10.1090/S0002-9939-1950-0036503-X
10.2307/1969087
10.1090/S0002-9904-1945-08370-0
10.1090/S0002-9939-1952-0046031-5
10.1134/S0081543809070165
10.15826/umj.2015.1.006
10.1023/A:1006593505036
10.1016/j.topol.2012.05.018
10.21136/CMJ.1971.101001
10.1155/S0161171294000980
10.1007/BF00058951
10.1007/BF01440953
10.4995/agt.2017.7048
10.1016/0166-8641(86)90009-X
10.1007/978-3-662-41914-4
10.1090/conm/486/09511
10.2140/pjm.1951.1.5
10.1155/S0161171293000122
10.2140/pjm.1965.15.961
ContentType Journal Article
DBID AAYXX
CITATION
DOA
DOI 10.4995/agt.2018.7630
DatabaseName CrossRef
DOAJ Directory of Open Access Journals
DatabaseTitle CrossRef
DatabaseTitleList
CrossRef
Database_xml – sequence: 1
  dbid: DOA
  name: DOAJ Directory of Open Access Journals
  url: https://www.doaj.org/
  sourceTypes: Open Website
DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
EISSN 1989-4147
EndPage 64
ExternalDocumentID oai_doaj_org_article_cf9d9416a23b4594b97ebde85f432689
10_4995_agt_2018_7630
GroupedDBID 5VS
AAYXX
ABDBF
ACUHS
ADBBV
ALMA_UNASSIGNED_HOLDINGS
AMVHM
BCNDV
CITATION
EBS
EJD
GROUPED_DOAJ
IPNFZ
J9A
KQ8
L7B
OK1
P2P
RIG
ID FETCH-LOGICAL-c342t-43e2b4c385ecf8a8d18b7c70b1e6d7c6bd0007f443bbd5aa8361a7475c7c40fc3
IEDL.DBID DOA
ISICitedReferencesCount 2
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000429424800004&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 1576-9402
IngestDate Fri Oct 03 12:52:34 EDT 2025
Tue Nov 18 22:20:42 EST 2025
Sat Nov 29 01:49:27 EST 2025
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 1
Language English
License http://creativecommons.org/licenses/by-nc-nd/4.0
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c342t-43e2b4c385ecf8a8d18b7c70b1e6d7c6bd0007f443bbd5aa8361a7475c7c40fc3
ORCID 0000-0002-0263-7270
OpenAccessLink https://doaj.org/article/cf9d9416a23b4594b97ebde85f432689
PageCount 10
ParticipantIDs doaj_primary_oai_doaj_org_article_cf9d9416a23b4594b97ebde85f432689
crossref_citationtrail_10_4995_agt_2018_7630
crossref_primary_10_4995_agt_2018_7630
PublicationCentury 2000
PublicationDate 2018-01-01
PublicationDateYYYYMMDD 2018-01-01
PublicationDate_xml – month: 01
  year: 2018
  text: 2018-01-01
  day: 01
PublicationDecade 2010
PublicationTitle Applied general topology
PublicationYear 2018
Publisher Universitat Politècnica de València
Publisher_xml – name: Universitat Politècnica de València
References Hoyle (ref4) 1971; 21
Di Concilio (ref1) 2000; 1-B
ref11
ref10
ref0
Khan (ref6) 1991; 5-B
Naimpally (ref9) 1966; 27
Osipov (ref10) 2011; 37
ref2
Osipov (ref11) 2017; 50
Kundu (ref7) 2006; 30
Gulick (ref3) 1972; 41
ref8
ref7
McCoy (ref8) 1988
ref9
Fletcher (ref2) 1982
ref4
Kelley (ref5) 1955
ref6
ref5
References_xml – ident: ref0
  doi: 10.1016/j.topol.2014.10.008
– ident: ref7
  doi: 10.1007/BF01961309
– ident: ref8
  doi: 10.2307/1969088
– ident: ref10
  doi: 10.1016/j.topol.2011.11.049
– ident: ref2
  doi: 10.7146/math.scand.a-11072
– ident: ref9
  doi: 10.1007/s10958-007-0258-3
– volume: 30
  start-page: 279
  year: 2006
  ident: ref7
  article-title: The pseudocompact-open topology on C(X)
  publication-title: Topology Proceedings Vol
– ident: ref6
  doi: 10.1515/dema-2013-0413
– ident: ref2
  doi: 10.1090/S0002-9939-1950-0036503-X
– ident: ref0
  doi: 10.2307/1969087
– volume: 27
  start-page: 768
  issn: 00193577
  year: 1966
  ident: ref9
  article-title: Function spaces of quasi-uniform spaces
  publication-title: Indag Math
– volume-title: Quasi-uniform spaces Lecture Notes in Pure and Applied Mathematics 77
  year: 1982
  ident: ref2
– ident: ref2
  doi: 10.1090/S0002-9904-1945-08370-0
– ident: ref4
  doi: 10.1090/S0002-9939-1952-0046031-5
– ident: ref9
  doi: 10.1134/S0081543809070165
– ident: ref10
  doi: 10.15826/umj.2015.1.006
– volume: 1-B
  start-page: 173
  issue: 8
  year: 2000
  ident: ref1
  article-title: Some proximal set-open topologies
  publication-title: Boll Unione Mat Ital
– volume-title: Topological properties of function spaces Lecture Notes in Math No 1315
  year: 1988
  ident: ref8
– volume: 5-B
  start-page: 727
  issue: 7
  year: 1991
  ident: ref6
  article-title: The σ-compact-open topology and its relatives on a space of vector-valued functions
  publication-title: Boll Unione Mat Italiana
– ident: ref7
  doi: 10.1023/A:1006593505036
– volume: 41
  start-page: 254
  issn: 00379565
  year: 1972
  ident: ref3
  article-title: Separability and semi-norm separability for spaces of bounded continuous functions
  publication-title: Bull Soc R Sci Liege
– ident: ref10
  doi: 10.1016/j.topol.2012.05.018
– volume: 37
  start-page: 205
  year: 2011
  ident: ref10
  article-title: The set-open topology
  publication-title: Topology Proc
– volume: 50
  start-page: 79
  year: 2017
  ident: ref11
  article-title: Uniformity of uniform convergence on the family of sets
  publication-title: Topology Proc
– volume: 21
  start-page: 31
  issn: 00114642
  year: 1971
  ident: ref4
  article-title: Function spaces for somewhat continuous functions
  publication-title: Czech Math J
  doi: 10.21136/CMJ.1971.101001
– volume-title: General topology D
  year: 1955
  ident: ref5
– ident: ref11
  doi: 10.1155/S0161171294000980
– ident: ref11
  doi: 10.1007/BF00058951
– ident: ref11
  doi: 10.1007/BF01440953
– ident: ref0
  doi: 10.4995/agt.2017.7048
– ident: ref7
  doi: 10.1016/0166-8641(86)90009-X
– ident: ref5
  doi: 10.1007/978-3-662-41914-4
– ident: ref7
  doi: 10.1090/conm/486/09511
– ident: ref0
  doi: 10.2140/pjm.1951.1.5
– ident: ref6
  doi: 10.1155/S0161171293000122
– ident: ref9
  doi: 10.2140/pjm.1965.15.961
SSID ssj0000396434
ssib044730014
Score 2.070694
Snippet Let X and Y be topological spaces, F(X,Y) the set of all functions from X into Y and C(X,Y) the set of all continuous functions in F(X,Y). We study various...
SourceID doaj
crossref
SourceType Open Website
Enrichment Source
Index Database
StartPage 55
SubjectTerms C-compact- open topology
pseudocompact-open topology
quasi-uniform convergence topology
right K- completeness
set-open topology
α-continuous function
Title Set-open topologies on function spaces
URI https://doaj.org/article/cf9d9416a23b4594b97ebde85f432689
Volume 19
WOSCitedRecordID wos000429424800004&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVAON
  databaseName: DOAJ Directory of Open Access Journals
  customDbUrl:
  eissn: 1989-4147
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0000396434
  issn: 1576-9402
  databaseCode: DOA
  dateStart: 20030101
  isFulltext: true
  titleUrlDefault: https://www.doaj.org/
  providerName: Directory of Open Access Journals
– providerCode: PRVHPJ
  databaseName: ROAD: Directory of Open Access Scholarly Resources
  customDbUrl:
  eissn: 1989-4147
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssib044730014
  issn: 1576-9402
  databaseCode: M~E
  dateStart: 20000101
  isFulltext: true
  titleUrlDefault: https://road.issn.org
  providerName: ISSN International Centre
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1NS8QwEA2yeNCD-InrFz3InqzbbqZNclRx8eIiqLC3kk8RpCu71d_vTFqX9SBevJZQ0pc0My-ZvMfYuUYezTUv0jKUEgkKbTQZZ9Iys06ZYMnhIppNiMlETqfqYcXqi2rCWnngFrihDcopzBr0iBsoFBglvHFeFgEw85Dx6l4m1AqZwpkEQDLs3flgXJM56U7FI2ZMsFMVy3pIcBMT_mKoX6iqMpeX-LNlPwLUio5_DDjjbbbVZYrJVdvDHbbm6122eb-UWV3sscGjb1Lyv0qa1usAaW8yqxMKVgR4gssFrgP77Hl8-3Rzl3bGB6nlMGpS4H5kwHJZeBukli6XRliRmdyXTtjSOArtAYAb4wqtJS9zjbygsMJCFiw_YL16VvtDliDBA11qkE5osMgtFDiOrNeR963Sqs8uvr-2sp0qOJlTvFXIDgicCsGpCJyKwOmzwbL5eyuH8VvDa4Ju2YhUrOMDHNuqG9vqr7E9-o-XHLMN6lW7bXLCes38w5-ydfvZvC7mZ3HafAFQxsHk
linkProvider Directory of Open Access Journals
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Set-open+topologies+on+function+spaces&rft.jtitle=Applied+general+topology&rft.au=Alqurashi%2C+Wafa+Khalaf&rft.au=Khan%2C+Liaqat+Ali&rft.au=Osipov%2C+Alexander+V.&rft.date=2018-01-01&rft.issn=1576-9402&rft.eissn=1989-4147&rft.volume=19&rft.issue=1&rft.spage=55&rft_id=info:doi/10.4995%2Fagt.2018.7630&rft.externalDBID=n%2Fa&rft.externalDocID=10_4995_agt_2018_7630
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1576-9402&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1576-9402&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1576-9402&client=summon