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dc.contributor.advisorCastellini, Gabriele
dc.contributor.authorCarrillo-Blanquicett, Alexis
dc.date.accessioned2019-04-15T12:05:54Z
dc.date.available2019-04-15T12:05:54Z
dc.date.issued2018-05
dc.identifier.urihttps://hdl.handle.net/handle/20.500.11801/1915
dc.description.abstractMotivated by the results obtained in the paper [1], concerning the notion of separation for an interior operator in topology, the notion of I-coseparation for an interior operator I in topology is introduced. A few examples that illustrate the behavior of this notion are presented for concrete interior operators in topology. Subsequently, it is determined under which topological properties this notion is closed. Later, it is obtained that in particular the I-coseparated topological spaces are closed under direct images of continuous functions and under quotient spaces but they are not closed under topological sums and topological subspaces. It is proved that the notion of I-coseparation generates a Galois connection between the class of all interior operators in topology and the conglomerate of all the subclasses of topological spaces. Using this result, a commutative diagram of Galois connections that shows the relationship between the notions of I-separation and I-coseparation is presented. Finally, it is proved that a characterization of the I-coseparated spaces in terms of separators, analogous to the one presented in [1] for the notion of I-separation, is not possible.en_US
dc.description.abstractMotivados por los resultados obtenidos en el artículo [1], respecto a la noción de separación para un operador de interior en topología, se introduce la noción de I-coseparación para un operador de interior topológico I. Se presentan algunos ejemplos que ilustran el comportamiento de esta noción de coseparación para operadores de interior topológicos concretos. Posteriormente se determina bajo qué propiedades topológicas esta noción es cerrada, de donde se obtiene en particular que los espacios I-coseparados son cerrados bajo la imagen directa de funciones continuas y bajo espacios cocientes, pero no son cerrados bajo suma topológica y subspacios topológicos. Se prueba que la noción de I-coseparación genera una conexión de Galois entre la clase de todos los operadores de interior topológicos y el conglomerado de todas las subclases de espacios topológicos y usando este resultado se presenta un diagrama conmutativo de conexiones de Galois que muestra la relación entre las nociones de I-separación e I-coseparación. Finalmente se prueba que una caracterización de los espacios I-coseparados, en términos de separadores, análoga a la presentada en [1] para la noción de I-separación, no es posible.en_US
dc.language.isoenen_US
dc.subjectLinear topological spacesen_US
dc.subjectGalois modules (Algebra)en_US
dc.subjectTopological spacesen_US
dc.subject.lcshTopological spacesen_US
dc.subject.lcshGalois theoryen_US
dc.titleCoseparation with respect to an interior operator in topologyen_US
dc.typeThesisen_US
dc.rights.licenseAll rights reserveden_US
dc.rights.holder(c) 2018 Alexis Carrillo Blanquicetten_US
dc.contributor.committeeOrtiz, Juan A.
dc.contributor.committeeRomero, Juan
dc.contributor.committeeRivera-Marrero, Olgamary
dc.contributor.representativeRios, Isabel
thesis.degree.levelM.S.en_US
thesis.degree.disciplinePure Mathematicsen_US
dc.contributor.collegeCollege of Arts and Sciences - Sciencesen_US
dc.contributor.departmentDepartment of Mathematicsen_US
dc.description.graduationSemesterSpringen_US
dc.description.graduationYear2018en_US


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