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Espacios pretopológicos: algunas aplicaciones


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Author: González Puntas, Gloria
Director: Ayala Gómez, Rafael
Vilches Alarcón, José Antonio
Department: Universidad de Sevilla. Departamento de Geometría y Topología
Date: 2018
Document type: Final Degree Work
Academic Title: Universidad de Sevilla. Grado en Matemáticas
Abstract: The goal of this work is to study the theory of pretopological spaces and some applications. Starting with the key notion of preclosure operator, we will introduce the basic concepts and results, which generalize the ideas and properties of point set topology. The different kinds of pretopological spaces are introduced and studied as well. Taking into account its importance in applications, a detailed analysis of pretopological spaces induced by binary relations is carried out. Finally, two particular applications of pretopology are presented: Modelling of complex networks and analysis of economical models.
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