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Between closed and Ig-closed sets
dc.contributor.author | Pachon Rubiano, Néstor Raúl | |
dc.date.accessioned | 2021-05-05T18:11:32Z | |
dc.date.accessioned | 2021-10-01T17:20:51Z | |
dc.date.available | 2021-05-05 | |
dc.date.available | 2021-10-01T17:20:51Z | |
dc.date.issued | 2018 | |
dc.identifier.issn | 1307-5543 | |
dc.identifier.uri | https://repositorio.escuelaing.edu.co/handle/001/1393 | |
dc.description.abstract | The concept of closed sets is a central object in general topology. In order to extend many of important properties of closed sets to a larger families, Norman Levine initiated the study of generalized closed sets. In this paper we introduce, via ideals, new generalizations of closed subsets, which are strong forms of the Ig-closed sets, called ρIg-closed sets and closed-I sets. We present some properties and applications of these new sets and compare the ρIg-closed sets and the closed-I sets with the g-closed sets introduced by Levine. We show that I-closed and closed-I are independent concepts, as well as I * -closed sets and closed-I concepts. | spa |
dc.description.abstract | El concepto de conjunto cerrado es un objeto central en la topología general. Con el fin de extender muchas de las propiedades importantes de los conjuntos cerrados a familias más amplias, Norman Levine inició el estudio de los conjuntos cerrados generalizados. En este trabajo introducimos, a través de ideales, nuevas generalizaciones de subconjuntos cerrados, que son formas fuertes de conjuntos cerrados. que son formas fuertes de los conjuntos cerrados Ig, llamados conjuntos cerrados ρIg y conjuntos cerrados-I. En presentamos algunas propiedades y aplicaciones de estos nuevos conjuntos y comparamos los conjuntos ρIg-cerrados y los conjuntos cerrados-I con los conjuntos g-cerrados introducidos por Levine. Demostramos que I-cerrado y cerrado-I son conceptos independientes, al igual que los conjuntos I * -cerrados y los conceptos cerrados-I. | spa |
dc.format.extent | 16 páginas | spa |
dc.format.mimetype | application/pdf | spa |
dc.language.iso | eng | spa |
dc.publisher | Business Global LLC | spa |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | spa |
dc.source | https://www.ejpam.com/index.php/ejpam/article/view/3131/608 | spa |
dc.title | Between closed and Ig-closed sets | spa |
dc.type | Artículo de revista | spa |
dc.description.notes | Néstor Raúl Pachón Rubiano Departamento de Matemáticas, Escuela Colombiana de Ingeniería, Bogotá, Colombia. Departamento de Matemáticas, Universidad Nacional, Bogotá, Colombia. | spa |
dc.description.notes | Email addresses: nestor.pachon@escuelaing.edu.co, nrpachonr@unal.edu.co (N.R. Pachón) | spa |
dc.type.version | info:eu-repo/semantics/publishedVersion | spa |
oaire.accessrights | http://purl.org/coar/access_right/c_abf2 | spa |
oaire.version | http://purl.org/coar/version/c_970fb48d4fbd8a85 | spa |
dc.contributor.researchgroup | Matemáticas | spa |
dc.identifier.doi | 10.29020/nybg.ejpam.v11i2.3131 | |
dc.identifier.url | doi.org/10.29020/nybg.ejpam.v11i2.3131 | |
dc.publisher.place | New York | eng |
dc.relation.citationedition | European Journal of Pure and Applied Mathematics, Vol. 11, No. 1, 2018, 299-314 | spa |
dc.relation.citationendpage | 314 | spa |
dc.relation.citationissue | 1 | spa |
dc.relation.citationstartpage | 299 | spa |
dc.relation.citationvolume | 11 | spa |
dc.relation.indexed | N/A | spa |
dc.relation.ispartofjournal | European Journal of Pure and Applied Mathematics | eng |
dc.relation.references | V. Renuka Devi and D. Sivaraj. A generalization of normal spaces. Archivum Mathematicum, 44:265–270, 2008. | eng |
dc.relation.references | S. Jafari and N. Rajesh. Generalized closed sets with respect to an ideal. Eur. Jour. of Pure and App. Math, 4(2):147–151, 2011. | eng |
dc.relation.references | D. Jancovic and T. R. Hamlett. New topologies from old via ideals. Amer. Math. Monthly, 97:295–310, 1990. | eng |
dc.relation.references | D. Jancovic and T. R. Hamlett. Compatible extensions of ideals. Bollettino U. M. I., (7):453–465, 1992. | eng |
dc.relation.references | N. Levine. Generalized closed sets in Topology. Rend. Circ. Mat. Palermo, 19(2):89– 96, 1970. | eng |
dc.relation.references | A. S. Mashhour, M. E. Abd El-Monsef, and S. N. El-Deep. On precontinuous and weak precontinuous mappings. Proc. Math. and Phys. Soc. of Egypt, 53:47–53, 1982 | eng |
dc.relation.references | Abd El Monsef, E. F. Lashien, and A. A. Nasef. On I-open sets and I-continuous functions. Kyungpook Math. Jour., 32(1):21–30, 1992. | eng |
dc.relation.references | R. L. Newcomb. Topologies which are compact modulo an ideal. PhD engthesis, Univ. of Calif. at Santa Barbara. California, 1967. | eng |
dc.relation.references | N. R. Pachón. New forms of strong compactness in terms of ideals. Int. Jour. of Pure and App. Math., 106(2):481–493, 2016. | eng |
dc.relation.references | N. R. Pachón. ρC(I)-compact and ρI-QHC spaces. Int. Jour. of Pure and App. Math., 108(2):199–214, 2016. | eng |
dc.relation.references | ] J. Porter and J. Thomas. On H-closed and minimal Hausdorff spaces. Trans. Amer. Math. Soc., 138:159–170, 1969. | eng |
dc.relation.references | ] R. Vaidyanathaswamy. The localization theory in set-topology. Proc. Indian Acad. Sci., 20:51–61, 1945. | eng |
dc.relation.references | G. Viglino. C-compact spaces. Duke Mathematical Journal, 36(4):761–764, 1969. | eng |
dc.relation.references | Suppose that X = ∪ α∈Λ Wα, where Wα ∈ τ ⊕ I for each α ∈ Λ. For all α ∈ Λ, there exist Vα ∈ τ and a collection {Ij}j∈Λα of elements in I, such that Wα = Vα ∪ ∪ j∈Λα Ij . Hence X = ∪ α∈Λ Vα ∪ ∪ α∈Λ ∪ j∈Λα Ij . Then X\ ∪ α∈Λ Vα ∈ I⊛ and since (X, τ, I ⊛) is ρI ⊛-compact, there exists Λ0 ⊆ Λ, finite, with X\ ∪ α∈Λ0 Vα ∈ I⊛. This implies that X\ ∪ α∈Λ0 Wα ∈ I⊛. | eng |
dc.relation.references | Suppose that X\ ∪ α∈Λ Vα ∈ I, where {Vα}α∈Λ is a collection of elements in τ . There exists I ∈ I such that X\ ∪ α∈Λ Vα = I, and so X = I∪ ∪ α∈Λ Vα. Given that (X, τ ⊕ I) is compact there exists Λ0 ⊆ Λ, finite, with X = I∪ ∪ α∈Λ0 Vα. Hence X\ ∪ α∈Λ0 Vα ⊆ I ∈ I and X\ ∪ α∈Λ0 Vα ∈ I. | eng |
dc.relation.references | Suppose that F\ ∪ α∈Λ Vα ∈ I, where {Vα}α∈Λ is a collection of elements in τ and F is closed in (X, τ ). There exists J ∈ I with F\ ∪ α∈Λ Vα = J, and so F ⊆ J ∪ ∪ α∈Λ Vα. Given that ( X, τ ⊕ I ) is C-compact and F is closed in ( X, τ ⊕ I ) , there exists Λ0 ⊆ Λ, finite, with F ⊆ adhτ⊕I (J) ∪ ∪ α∈Λ0 adhτ⊕I (Vα) ⊆ J ∪ ∪ α∈Λ0 Vα. Hence F\ ∪ α∈Λ0 Vα ⊆ J ∈ I and F\ ∪ α∈Λ0 Vα ∈ I. Parts (2) and (5) have similar demonstrations. □ | eng |
dc.rights.accessrights | info:eu-repo/semantics/openAccess | spa |
dc.rights.creativecommons | Atribución 4.0 Internacional (CC BY 4.0) | spa |
dc.subject.armarc | Mateméticas | |
dc.subject.armarc | Acciones de grupos (Matemáticas) | |
dc.subject.proposal | g-closed | spa |
dc.subject.proposal | Ig-closed | spa |
dc.subject.proposal | I-compact | spa |
dc.subject.proposal | I-normal | spa |
dc.subject.proposal | I-QHC | spa |
dc.subject.proposal | ρC(I)-compact. | spa |
dc.subject.proposal | g-closed | spa |
dc.subject.proposal | Ig-closed | spa |
dc.subject.proposal | I-compact | spa |
dc.subject.proposal | I-normal | spa |
dc.subject.proposal | I-QHC | spa |
dc.subject.proposal | ρC(I)-compact. | spa |
dc.type.coar | http://purl.org/coar/resource_type/c_2df8fbb1 | spa |
dc.type.content | Text | spa |
dc.type.driver | info:eu-repo/semantics/article | spa |
dc.type.redcol | http://purl.org/redcol/resource_type/ART | spa |
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