On contra λsi-continuous functions and their applications

In this work, we introduce and study the classes of contra ΛsI-continuous,contra quasi-ΛsI-continuous and contra ΛsI-irresolute functions in a topological spaceendowed with an ideal. We investigate the relationships among these functions andtheir respective characterizations. Also, we analyze the be...

Full description

Autores:
Granados, Carlos
Sanabria, José
ROSAS, ENNIS
Carpintero, Carlos
Tipo de recurso:
Article of journal
Fecha de publicación:
2021
Institución:
Corporación Universidad de la Costa
Repositorio:
REDICUC - Repositorio CUC
Idioma:
eng
OAI Identifier:
oai:repositorio.cuc.edu.co:11323/8208
Acceso en línea:
https://hdl.handle.net/11323/8208
https://doi.org/10.28919/jmcs/5561
https://repositorio.cuc.edu.co/
Palabra clave:
ideal
semi-I-open set
ΛsI-closed set
Contra ΛsI-irresolute function
Rights
openAccess
License
CC0 1.0 Universal
id RCUC2_6409fbebb783531d9ce2670d9f2e4634
oai_identifier_str oai:repositorio.cuc.edu.co:11323/8208
network_acronym_str RCUC2
network_name_str REDICUC - Repositorio CUC
repository_id_str
dc.title.eng.fl_str_mv On contra λsi-continuous functions and their applications
title On contra λsi-continuous functions and their applications
spellingShingle On contra λsi-continuous functions and their applications
ideal
semi-I-open set
ΛsI-closed set
Contra ΛsI-irresolute function
title_short On contra λsi-continuous functions and their applications
title_full On contra λsi-continuous functions and their applications
title_fullStr On contra λsi-continuous functions and their applications
title_full_unstemmed On contra λsi-continuous functions and their applications
title_sort On contra λsi-continuous functions and their applications
dc.creator.fl_str_mv Granados, Carlos
Sanabria, José
ROSAS, ENNIS
Carpintero, Carlos
dc.contributor.author.spa.fl_str_mv Granados, Carlos
Sanabria, José
ROSAS, ENNIS
Carpintero, Carlos
dc.subject.eng.fl_str_mv ideal
semi-I-open set
ΛsI-closed set
Contra ΛsI-irresolute function
topic ideal
semi-I-open set
ΛsI-closed set
Contra ΛsI-irresolute function
description In this work, we introduce and study the classes of contra ΛsI-continuous,contra quasi-ΛsI-continuous and contra ΛsI-irresolute functions in a topological spaceendowed with an ideal. We investigate the relationships among these functions andtheir respective characterizations. Also, we analyze the behavior of certain topologicalnotions under direct and inverse images of these new classes of functions.
publishDate 2021
dc.date.accessioned.none.fl_str_mv 2021-04-27T20:56:32Z
dc.date.available.none.fl_str_mv 2021-04-27T20:56:32Z
dc.date.issued.none.fl_str_mv 2021
dc.type.spa.fl_str_mv Artículo de revista
dc.type.coar.fl_str_mv http://purl.org/coar/resource_type/c_2df8fbb1
dc.type.coar.spa.fl_str_mv http://purl.org/coar/resource_type/c_6501
dc.type.content.spa.fl_str_mv Text
dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/article
dc.type.redcol.spa.fl_str_mv http://purl.org/redcol/resource_type/ART
dc.type.version.spa.fl_str_mv info:eu-repo/semantics/acceptedVersion
format http://purl.org/coar/resource_type/c_6501
status_str acceptedVersion
dc.identifier.issn.spa.fl_str_mv 1927-5307
dc.identifier.uri.spa.fl_str_mv https://hdl.handle.net/11323/8208
dc.identifier.doi.spa.fl_str_mv https://doi.org/10.28919/jmcs/5561
dc.identifier.instname.spa.fl_str_mv Corporación Universidad de la Costa
dc.identifier.reponame.spa.fl_str_mv REDICUC - Repositorio CUC
dc.identifier.repourl.spa.fl_str_mv https://repositorio.cuc.edu.co/
identifier_str_mv 1927-5307
Corporación Universidad de la Costa
REDICUC - Repositorio CUC
url https://hdl.handle.net/11323/8208
https://doi.org/10.28919/jmcs/5561
https://repositorio.cuc.edu.co/
dc.language.iso.none.fl_str_mv eng
language eng
dc.relation.references.spa.fl_str_mv [1] J. Dontchev, Contra-continuous functions and strongly S-closed spaces, Int. J. Math. & Math. Sci. 19 (2) (1996), 303-310.
[2] J. Dontchev, Survey on preopen sets , The Proceedings of the Yatsushiro Topological Conference 22-23 August 1998, pp. 1-18.
[3] E. Hatir and T. Noiri, On decompositions of continuity via idealization , Acta. Math. Hungar. 96 (4) (2002), 341-349.
[4] D. S. Jankovic and T. R. Hamlett, New topologies from old via ideals , Amer. Math. Monthly, 97 (1990), 295-310.
[5] K. Kuratowski, Topologie I, Monografie Matematyczne tom 3, PWN-Polish Scientific Publishers, Warszawa, 1933.
[6] J. Sanabria, E. Rosas and C. Carpintero, On ΛsI -sets and the related notions in ideal topological spaces, Math. Slovaca 63 (6) (2013), 1403-1411.
[7] J. Sanabria, E. Acosta, E. Rosas and C. Carpintero, Continuity via ΛsI-open sets, Cubo 16 (1) (2015), 75-84.
[8] R. Staum, The algebra of bounded continuous functions into a non archimedian field, Pacific J. Math. 50 (1) (1974), 169-185.
[9] S. Willard, General Topology, Addison-Wesley Publishing Company, Reading, Massachusetts, 1970.
dc.rights.spa.fl_str_mv CC0 1.0 Universal
dc.rights.uri.spa.fl_str_mv http://creativecommons.org/publicdomain/zero/1.0/
dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
dc.rights.coar.spa.fl_str_mv http://purl.org/coar/access_right/c_abf2
rights_invalid_str_mv CC0 1.0 Universal
http://creativecommons.org/publicdomain/zero/1.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.mimetype.spa.fl_str_mv application/pdf
dc.publisher.spa.fl_str_mv Corporación Universidad de la Costa
dc.source.spa.fl_str_mv Journal of Mathematical and Computational Science
institution Corporación Universidad de la Costa
dc.source.url.spa.fl_str_mv http://scik.org/index.php/jmcs/article/view/5561
bitstream.url.fl_str_mv https://repositorio.cuc.edu.co/bitstreams/cc1e7a4b-904a-4c7d-8af8-b58ecbb74c34/download
https://repositorio.cuc.edu.co/bitstreams/fcbd3bb7-5f71-4fa9-9521-036083603264/download
https://repositorio.cuc.edu.co/bitstreams/4cdbf9bc-0a98-4cf6-9cd3-1c4f38cd8acb/download
https://repositorio.cuc.edu.co/bitstreams/1d3f540d-7e44-4991-8fc1-91749915e618/download
https://repositorio.cuc.edu.co/bitstreams/d1815321-a272-4036-ae46-fe090e62b923/download
https://repositorio.cuc.edu.co/bitstreams/c720fce4-a99a-4232-bba1-a2f6cf500085/download
https://repositorio.cuc.edu.co/bitstreams/72b91fe6-1117-4754-9cd8-1e837ac86c5c/download
https://repositorio.cuc.edu.co/bitstreams/5d2271db-a343-47c9-8fa5-e01d20423a57/download
https://repositorio.cuc.edu.co/bitstreams/8ff963d4-56ad-41d5-b4b4-01c648e19864/download
https://repositorio.cuc.edu.co/bitstreams/f64c5bf3-ef02-4cd0-86b0-e88cb8e6b6d1/download
bitstream.checksum.fl_str_mv 8451147d341ca6fed6f9ffa831e828eb
3b96ff4e5461b7c73b43844ffe7ff070
42fd4ad1e89814f5e4a476b409eb708c
e30e9215131d99561d40d6b0abbe9bad
1fe9c072cb449d5fe8a12f5789d8bf60
6d6171e41ff34c512c0f8da571610dce
1fe9c072cb449d5fe8a12f5789d8bf60
6d6171e41ff34c512c0f8da571610dce
ecdfef286e5db9859fab16ab2c1ae257
69810f6f6e424fc6b872afdbf064ff77
bitstream.checksumAlgorithm.fl_str_mv MD5
MD5
MD5
MD5
MD5
MD5
MD5
MD5
MD5
MD5
repository.name.fl_str_mv Repositorio de la Universidad de la Costa CUC
repository.mail.fl_str_mv repdigital@cuc.edu.co
_version_ 1811760822487089152
spelling Granados, CarlosSanabria, JoséROSAS, ENNISCarpintero, Carlos2021-04-27T20:56:32Z2021-04-27T20:56:32Z20211927-5307https://hdl.handle.net/11323/8208https://doi.org/10.28919/jmcs/5561Corporación Universidad de la CostaREDICUC - Repositorio CUChttps://repositorio.cuc.edu.co/In this work, we introduce and study the classes of contra ΛsI-continuous,contra quasi-ΛsI-continuous and contra ΛsI-irresolute functions in a topological spaceendowed with an ideal. We investigate the relationships among these functions andtheir respective characterizations. Also, we analyze the behavior of certain topologicalnotions under direct and inverse images of these new classes of functions.Granados, Carlos-will be generated-orcid-0000-0002-7754-1468-600Sanabria, JoséROSAS, ENNIS-will be generated-orcid-0000-0001-8123-9344-600Carpintero, Carlos-will be generated-orcid-0000-0003-3831-952X-600application/pdfengCorporación Universidad de la CostaCC0 1.0 Universalhttp://creativecommons.org/publicdomain/zero/1.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Journal of Mathematical and Computational Sciencehttp://scik.org/index.php/jmcs/article/view/5561idealsemi-I-open setΛsI-closed setContra ΛsI-irresolute functionOn contra λsi-continuous functions and their applicationsArtículo de revistahttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTinfo:eu-repo/semantics/acceptedVersion[1] J. Dontchev, Contra-continuous functions and strongly S-closed spaces, Int. J. Math. & Math. Sci. 19 (2) (1996), 303-310.[2] J. Dontchev, Survey on preopen sets , The Proceedings of the Yatsushiro Topological Conference 22-23 August 1998, pp. 1-18.[3] E. Hatir and T. Noiri, On decompositions of continuity via idealization , Acta. Math. Hungar. 96 (4) (2002), 341-349.[4] D. S. Jankovic and T. R. Hamlett, New topologies from old via ideals , Amer. Math. Monthly, 97 (1990), 295-310.[5] K. Kuratowski, Topologie I, Monografie Matematyczne tom 3, PWN-Polish Scientific Publishers, Warszawa, 1933.[6] J. Sanabria, E. Rosas and C. Carpintero, On ΛsI -sets and the related notions in ideal topological spaces, Math. Slovaca 63 (6) (2013), 1403-1411.[7] J. Sanabria, E. Acosta, E. Rosas and C. Carpintero, Continuity via ΛsI-open sets, Cubo 16 (1) (2015), 75-84.[8] R. Staum, The algebra of bounded continuous functions into a non archimedian field, Pacific J. Math. 50 (1) (1974), 169-185.[9] S. Willard, General Topology, Addison-Wesley Publishing Company, Reading, Massachusetts, 1970.PublicationORIGINAL5561-12700-1-PB.pdf5561-12700-1-PB.pdfapplication/pdf145169https://repositorio.cuc.edu.co/bitstreams/cc1e7a4b-904a-4c7d-8af8-b58ecbb74c34/download8451147d341ca6fed6f9ffa831e828ebMD55On contra λsi-continuous functions and theirapplications.pdfOn contra λsi-continuous functions and theirapplications.pdfapplication/pdf64143https://repositorio.cuc.edu.co/bitstreams/fcbd3bb7-5f71-4fa9-9521-036083603264/download3b96ff4e5461b7c73b43844ffe7ff070MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8701https://repositorio.cuc.edu.co/bitstreams/4cdbf9bc-0a98-4cf6-9cd3-1c4f38cd8acb/download42fd4ad1e89814f5e4a476b409eb708cMD52LICENSElicense.txtlicense.txttext/plain; charset=utf-83196https://repositorio.cuc.edu.co/bitstreams/1d3f540d-7e44-4991-8fc1-91749915e618/downloade30e9215131d99561d40d6b0abbe9badMD53THUMBNAIL5561-12700-1-PB.pdf.jpg5561-12700-1-PB.pdf.jpgimage/jpeg42655https://repositorio.cuc.edu.co/bitstreams/d1815321-a272-4036-ae46-fe090e62b923/download1fe9c072cb449d5fe8a12f5789d8bf60MD56On contra λsi-continuous functions and theirapplications.pdf.jpgOn contra λsi-continuous functions and theirapplications.pdf.jpgimage/jpeg33875https://repositorio.cuc.edu.co/bitstreams/c720fce4-a99a-4232-bba1-a2f6cf500085/download6d6171e41ff34c512c0f8da571610dceMD57THUMBNAIL5561-12700-1-PB.pdf.jpg5561-12700-1-PB.pdf.jpgimage/jpeg42655https://repositorio.cuc.edu.co/bitstreams/72b91fe6-1117-4754-9cd8-1e837ac86c5c/download1fe9c072cb449d5fe8a12f5789d8bf60MD56On contra λsi-continuous functions and theirapplications.pdf.jpgOn contra λsi-continuous functions and theirapplications.pdf.jpgimage/jpeg33875https://repositorio.cuc.edu.co/bitstreams/5d2271db-a343-47c9-8fa5-e01d20423a57/download6d6171e41ff34c512c0f8da571610dceMD57TEXT5561-12700-1-PB.pdf.txt5561-12700-1-PB.pdf.txttext/plain27430https://repositorio.cuc.edu.co/bitstreams/8ff963d4-56ad-41d5-b4b4-01c648e19864/downloadecdfef286e5db9859fab16ab2c1ae257MD58On contra λsi-continuous functions and theirapplications.pdf.txtOn contra λsi-continuous functions and theirapplications.pdf.txttext/plain1906https://repositorio.cuc.edu.co/bitstreams/f64c5bf3-ef02-4cd0-86b0-e88cb8e6b6d1/download69810f6f6e424fc6b872afdbf064ff77MD5911323/8208oai:repositorio.cuc.edu.co:11323/82082024-09-17 14:05:22.486http://creativecommons.org/publicdomain/zero/1.0/CC0 1.0 Universalopen.accesshttps://repositorio.cuc.edu.coRepositorio de la Universidad de la Costa CUCrepdigital@cuc.edu.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