Bitopological weak continuous multifunctions
In this paper, we introduce and study the concept of a new type of weak continuous multifunctions between bitopological spaces.
- Autores:
-
Carpintero, Carlos R
Rajesh, Neelamegarajan
ROSAS, ENNIS
Rajalakshmi, Raji
- 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:11323/9474
- Acceso en línea:
- https://hdl.handle.net/11323/9474
https://repositorio.cuc.edu.co/
- Palabra clave:
- Bitopological spaces
Open set
(i; j)-upper weakly continuous function
- Rights
- openAccess
- License
- Atribución 4.0 Internacional (CC BY 4.0)
| id |
RCUC2_4e96c67fa508ad579a3f7c58c84dab0f |
|---|---|
| oai_identifier_str |
oai:repositorio.cuc.edu.co:11323/9474 |
| network_acronym_str |
RCUC2 |
| network_name_str |
REDICUC - Repositorio CUC |
| repository_id_str |
|
| dc.title.eng.fl_str_mv |
Bitopological weak continuous multifunctions |
| title |
Bitopological weak continuous multifunctions |
| spellingShingle |
Bitopological weak continuous multifunctions Bitopological spaces Open set (i; j)-upper weakly continuous function |
| title_short |
Bitopological weak continuous multifunctions |
| title_full |
Bitopological weak continuous multifunctions |
| title_fullStr |
Bitopological weak continuous multifunctions |
| title_full_unstemmed |
Bitopological weak continuous multifunctions |
| title_sort |
Bitopological weak continuous multifunctions |
| dc.creator.fl_str_mv |
Carpintero, Carlos R Rajesh, Neelamegarajan ROSAS, ENNIS Rajalakshmi, Raji |
| dc.contributor.author.spa.fl_str_mv |
Carpintero, Carlos R Rajesh, Neelamegarajan ROSAS, ENNIS Rajalakshmi, Raji |
| dc.subject.proposal.eng.fl_str_mv |
Bitopological spaces Open set (i; j)-upper weakly continuous function |
| topic |
Bitopological spaces Open set (i; j)-upper weakly continuous function |
| description |
In this paper, we introduce and study the concept of a new type of weak continuous multifunctions between bitopological spaces. |
| publishDate |
2021 |
| dc.date.issued.none.fl_str_mv |
2021 |
| dc.date.accessioned.none.fl_str_mv |
2022-08-24T23:59:09Z |
| dc.date.available.none.fl_str_mv |
2022-08-24T23:59:09Z |
| 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.coarversion.fl_str_mv |
http://purl.org/coar/version/c_970fb48d4fbd8a85 |
| 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 |
| format |
http://purl.org/coar/resource_type/c_6501 |
| dc.identifier.issn.spa.fl_str_mv |
2346-8092 |
| dc.identifier.uri.spa.fl_str_mv |
https://hdl.handle.net/11323/9474 |
| dc.identifier.eissn.spa.fl_str_mv |
2588-9028 |
| 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 |
2346-8092 2588-9028 Corporación Universidad de la Costa REDICUC - Repositorio CUC |
| url |
https://hdl.handle.net/11323/9474 https://repositorio.cuc.edu.co/ |
| dc.language.iso.none.fl_str_mv |
eng |
| language |
eng |
| dc.relation.ispartofjournal.spa.fl_str_mv |
Transactions of A. Razmadze Mathematical Institute |
| dc.relation.references.spa.fl_str_mv |
1. S. Al-Ghour, S. Issa, On u-ω-open and q-ω-open sets in bitopological spaces. Missouri J. Math. Sci. 24 (2012), no. 1, 37–53. 2. A. Al-Omari, T. Noiri, M. S. M. Noorani, Weak and strong forms of ω-continuous functions. Int. J. Math. Math. Sci. 2009, Art. ID 174042, 12 pp. 3. A. Al-Omari, M. S. M. Noorani, Contra-ω-continuous and almost ω-continuous functions. Int. J. Math. Math. Sci. 2007, Article ID 40469, 13 pp. 4. K. Al-Zoubi, On generalized ω-closed sets. Int. J. Math. Math. Sci. 13 (2005), 2011–2021. 5. K. Al-Zoubi, B. Al-Nashef, The topology of ω-open subsets. Al-Manarah 9 (2003), 169–179. 6. T. Banzaru, Multivalued mappings and M-product spaces. (Romanian) Bul. ti. Tehn. Inst. Politehn. Timioara Ser. Mat.-Fiz.-Mec. Teoret. Apl. 17(31) (1972), no. 1, 17–23. 7. S. Bose, S. P. Sinha, Almost open, almost closed, θ-continuous and almost quasicompact mappings in bitopological spaces. Bull. Calcutta Math. Soc. 73 (1981), no. 6, 345–354. 8. E. Ekici, S. Jafari, S. P. Moshokoa, On a weaker form of ω-continuity. An. Univ. Craiova Ser. Mat. Inform. 37 (2010), no. 2, 38–46. 9. H. Z. Hdeib, ω-closed mappings. Rev. Colombiana Mat. 16 (1982), no. 1-2, 65–78. 10. H. Z. Hdeib, ω-continuous functions. Dirasat, 16 (1989), no. 2, 136–142. 11. C. G. Kariofillis, On pairwise almost compactness. Ann. Soc. Sci. Bruxelles Sr. I 100 (1986), no. 4, 129–137 (1988). 12. F. H. Khedr, S. M. Al. Areefi, T. Noiri, Precontinuity and semiprecontinuity in bitopological spaces. Indian J. Pure Appl. Math. 23 (1992), no. 9, 625–633. 13. E. Rosas, C. Carpintero, N. Rajesh, S. Shanthi, Near ω-continuous multifunctions on bitopological spaces. royecciones 38 (2019), no. 4, 691–698. 14. A. Rychlewicz, On almost nearly continuity with reference to multifunctions in bitopological spaces. Novi Sad J. Math. 38 (2008), no. 2, 5–14. |
| dc.relation.citationendpage.spa.fl_str_mv |
335 |
| dc.relation.citationstartpage.spa.fl_str_mv |
331 |
| dc.relation.citationissue.spa.fl_str_mv |
3 |
| dc.relation.citationvolume.spa.fl_str_mv |
175 |
| dc.rights.spa.fl_str_mv |
Atribución 4.0 Internacional (CC BY 4.0) © Copyright 2019, Razmadze Mathematical Institute. |
| dc.rights.uri.spa.fl_str_mv |
https://creativecommons.org/licenses/by/4.0/ |
| 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 |
Atribución 4.0 Internacional (CC BY 4.0) © Copyright 2019, Razmadze Mathematical Institute. https://creativecommons.org/licenses/by/4.0/ http://purl.org/coar/access_right/c_abf2 |
| eu_rights_str_mv |
openAccess |
| dc.format.extent.spa.fl_str_mv |
5 páginas |
| dc.format.mimetype.spa.fl_str_mv |
application/pdf |
| dc.publisher.spa.fl_str_mv |
Elsevier BV |
| dc.publisher.place.spa.fl_str_mv |
Georgia |
| institution |
Corporación Universidad de la Costa |
| dc.source.url.spa.fl_str_mv |
http://rmi.ge/transactions/TRMI-volumes/175-3/v175(3)-5.pdf |
| bitstream.url.fl_str_mv |
https://repositorio.cuc.edu.co/bitstreams/069ce974-c2b4-4276-99c0-1032b799cc6e/download https://repositorio.cuc.edu.co/bitstreams/4f5ac9c5-a98f-4fac-acaf-a1e00576b0d9/download https://repositorio.cuc.edu.co/bitstreams/058a816c-a618-48bd-a06c-f6e1ac8526ba/download https://repositorio.cuc.edu.co/bitstreams/dd5271b3-7d5d-4188-8023-77da9aa4d9f6/download |
| bitstream.checksum.fl_str_mv |
3c7e278a50a2baacf7f527ecd12a7575 e30e9215131d99561d40d6b0abbe9bad 961e2e400b543e058e75401126802522 2da880f90ce7ec00c9200aee1e286af2 |
| bitstream.checksumAlgorithm.fl_str_mv |
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_ |
1811760843916836864 |
| spelling |
Carpintero, Carlos RRajesh, NeelamegarajanROSAS, ENNISRajalakshmi, Raji2022-08-24T23:59:09Z2022-08-24T23:59:09Z20212346-8092https://hdl.handle.net/11323/94742588-9028Corporación Universidad de la CostaREDICUC - Repositorio CUChttps://repositorio.cuc.edu.co/In this paper, we introduce and study the concept of a new type of weak continuous multifunctions between bitopological spaces.5 páginasapplication/pdfengElsevier BVGeorgiaAtribución 4.0 Internacional (CC BY 4.0)© Copyright 2019, Razmadze Mathematical Institute.https://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Bitopological weak continuous multifunctionsArtículo 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/ARThttp://purl.org/coar/version/c_970fb48d4fbd8a85http://rmi.ge/transactions/TRMI-volumes/175-3/v175(3)-5.pdfTransactions of A. Razmadze Mathematical Institute1. S. Al-Ghour, S. Issa, On u-ω-open and q-ω-open sets in bitopological spaces. Missouri J. Math. Sci. 24 (2012), no. 1, 37–53.2. A. Al-Omari, T. Noiri, M. S. M. Noorani, Weak and strong forms of ω-continuous functions. Int. J. Math. Math. Sci. 2009, Art. ID 174042, 12 pp.3. A. Al-Omari, M. S. M. Noorani, Contra-ω-continuous and almost ω-continuous functions. Int. J. Math. Math. Sci. 2007, Article ID 40469, 13 pp.4. K. Al-Zoubi, On generalized ω-closed sets. Int. J. Math. Math. Sci. 13 (2005), 2011–2021.5. K. Al-Zoubi, B. Al-Nashef, The topology of ω-open subsets. Al-Manarah 9 (2003), 169–179.6. T. Banzaru, Multivalued mappings and M-product spaces. (Romanian) Bul. ti. Tehn. Inst. Politehn. Timioara Ser. Mat.-Fiz.-Mec. Teoret. Apl. 17(31) (1972), no. 1, 17–23.7. S. Bose, S. P. Sinha, Almost open, almost closed, θ-continuous and almost quasicompact mappings in bitopological spaces. Bull. Calcutta Math. Soc. 73 (1981), no. 6, 345–354.8. E. Ekici, S. Jafari, S. P. Moshokoa, On a weaker form of ω-continuity. An. Univ. Craiova Ser. Mat. Inform. 37 (2010), no. 2, 38–46.9. H. Z. Hdeib, ω-closed mappings. Rev. Colombiana Mat. 16 (1982), no. 1-2, 65–78.10. H. Z. Hdeib, ω-continuous functions. Dirasat, 16 (1989), no. 2, 136–142.11. C. G. Kariofillis, On pairwise almost compactness. Ann. Soc. Sci. Bruxelles Sr. I 100 (1986), no. 4, 129–137 (1988).12. F. H. Khedr, S. M. Al. Areefi, T. Noiri, Precontinuity and semiprecontinuity in bitopological spaces. Indian J. Pure Appl. Math. 23 (1992), no. 9, 625–633.13. E. Rosas, C. Carpintero, N. Rajesh, S. Shanthi, Near ω-continuous multifunctions on bitopological spaces. royecciones 38 (2019), no. 4, 691–698.14. A. Rychlewicz, On almost nearly continuity with reference to multifunctions in bitopological spaces. Novi Sad J. Math. 38 (2008), no. 2, 5–14.3353313175Bitopological spacesOpen set(i; j)-upper weakly continuous functionPublicationORIGINALBITOPOLOGICAL WEAK CONTINUOUS MULTIFUNCTIONS.pdfBITOPOLOGICAL WEAK CONTINUOUS MULTIFUNCTIONS.pdfapplication/pdf251095https://repositorio.cuc.edu.co/bitstreams/069ce974-c2b4-4276-99c0-1032b799cc6e/download3c7e278a50a2baacf7f527ecd12a7575MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-83196https://repositorio.cuc.edu.co/bitstreams/4f5ac9c5-a98f-4fac-acaf-a1e00576b0d9/downloade30e9215131d99561d40d6b0abbe9badMD52TEXTBITOPOLOGICAL WEAK CONTINUOUS MULTIFUNCTIONS.pdf.txtBITOPOLOGICAL WEAK CONTINUOUS MULTIFUNCTIONS.pdf.txttext/plain17703https://repositorio.cuc.edu.co/bitstreams/058a816c-a618-48bd-a06c-f6e1ac8526ba/download961e2e400b543e058e75401126802522MD53THUMBNAILBITOPOLOGICAL WEAK CONTINUOUS MULTIFUNCTIONS.pdf.jpgBITOPOLOGICAL WEAK CONTINUOUS MULTIFUNCTIONS.pdf.jpgimage/jpeg13216https://repositorio.cuc.edu.co/bitstreams/dd5271b3-7d5d-4188-8023-77da9aa4d9f6/download2da880f90ce7ec00c9200aee1e286af2MD5411323/9474oai:repositorio.cuc.edu.co:11323/94742024-09-17 14:09:38.237https://creativecommons.org/licenses/by/4.0/Atribución 4.0 Internacional (CC BY 4.0)open.accesshttps://repositorio.cuc.edu.coRepositorio de la Universidad de la Costa CUCrepdigital@cuc.edu.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 |