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dc.contributor.advisorCastellini, Gabriele
dc.contributor.authorMurcia-Rodríguez, Edwin G.
dc.description.abstractA notion of separation with respect to an interior operator in topology is introduced. After concrete examples, some properties of separation are presented. In particular, closure of separation with respect to subspaces and products is proved. This notion of separation with respect to an interior operator gives rise to a Galois connection between the collection of all Topological Spaces and the collection of all Interior Operators in Topology. Characterizations of the fixed points of this Galois connection are given. An equivalent definition of separation is introduced that makes possible a generalization to other categories as well. Examples are provided.
dc.description.abstractSe introduce una noción de separación con respecto a un operador de interior topológico. Después de proporcionar ejemplos concretos, se presentan algunas propiedades. En particular se demuestra que la separación es cerrada con respecto a subespacios y productos. Esta noción de separación con respecto a un operador de interior da origen a una conexión de Galois entre la colección de Espacios Topológicos y la colección de Operadores de Interior en Topología. Se presentan caracterizaciones de los puntos fijos de esta conexión de Galois. Se introduce una definición equivalente de separación que hace posible una generalización a otras categorías. Se presentan algunos ejemplos.
dc.subjectGalois connectionen_US
dc.subjectFixed pointsen_US
dc.subject.lcshClosure operatorsen_US
dc.subject.lcshGalois theoryen_US
dc.subject.lcshTopological spacesen_US
dc.subject.lcshFixed point theoryen_US
dc.titleThe notion of separation for interior operators in topologyen_US
dc.rights.licenseAll rights reserveden_US
dc.rights.holder(c)2010 Edwin G. Murcia Rodríguezen_US
dc.contributor.committeeBarety, Julio E.
dc.contributor.committeeCáceres Duque, Luis F.
dc.contributor.representativeSeguel, Jaime Mathematicsen_US
dc.contributor.collegeCollege of Arts and Sciences - Sciencesen_US
dc.contributor.departmentDepartment of Mathematicsen_US

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