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dc.contributor.advisorCastellini, Gabriele
dc.contributor.authorMedina-Droz, Emanuel
dc.date.accessioned2017-12-08T14:08:53Z
dc.date.available2017-12-08T14:08:53Z
dc.date.issued2015-05
dc.identifier.urihttps://hdl.handle.net/20.500.11801/116
dc.description.abstractA previously introduced notion of categorical interior operator is studied in the category of groups. The main purpose of this research is to try to find out how many of the general results that hold for a categorical interior operator in topology can be proved in the category of groups, paying particular attention to the notions of connectedness and disconnectedness. Some general properties of interior operators in groups are studied and the notions of discrete, indiscrete, connected and disconnected groups with respect to an interior operator are introduced. The main objective of this work is to discover whether by means of the above notions, a commutative diagram of Galois connections previously presented in the category of topological spaces, can be reconstructed in the group environment. However, unlike the topological case, the lack of commutativity between inverse images and suprema created a big obstacle that, for the time being, could be overcome only by means of two conjectures. Examples are provided.
dc.description.abstractUna noción introducida previamente de operador de interior de categorías es estudiado en la categoría de grupos. El propósito principal de esta investigación es intentar hallar cuántos de los resultados generales que se tienen para un operador de interior de categorías en topología pueden ser demostrados en la categoría de grupos, prestando especial atención a las nociones de conexidad y desconexidad. Algunas propiedades generales de los operadores de interior en grupos son estudiadas y las nociones de grupos discretos, indiscretos, conexos y desconexos son introducidas con respecto a un operador de interior. El objetivo principal de este trabajo es descubrir si por medio de las nociones mencionadas, un diagrama conmutativo de conexiones de Galois previamente presentado en la categoría de espacios topológicos, puede reconstruirse en el entorno de los grupos. Sin embargo, a diferencia del caso topológico, la falta de conmutatividad entre las imágenes inversas y supremos creó un gran obstáculo que, por el momento, podría ser superado sólo por medio de dos conjeturas. Se proporcionan ejemplos.
dc.language.isoenen_US
dc.subjectInterior operatorsen_US
dc.subjectGroupsen_US
dc.subject.lcshTopologyen_US
dc.subject.lcshCategories (Mathematics)en_US
dc.subject.lcshDiscrete groupsen_US
dc.subject.lcshGalois theoryen_US
dc.subject.lcshGroup theoryen_US
dc.titleInterior operators in the category of groupsen_US
dc.typeThesisen_US
dc.rights.licenseAll rights reserveden_US
dc.rights.holder(c)2015 Emanuel Medina Drozen_US
dc.contributor.committeeCaceres Duque, Luis F.
dc.contributor.committeeOrtiz Navarro, Juan A.
dc.contributor.representativeBaiges Valentin, Ivan J.
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.graduationYear2015en_US


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