Sobre la caracterización del álgebra topológica de las funciones reales y continuas sobre un espacio topológico
- Pulgarín García, Antonio Ángel
- Francisco Montalvo Durán Director
- Batildo Requejo Fernández Director
Universidade de defensa: Universidad de Extremadura
Fecha de defensa: 13 de setembro de 2003
- José Luis Blasco Olcina Presidente/a
- María Ángeles Mulero Díaz Secretario/a
- Manuel Sanchís López Vogal
- María Isabel Garrido Carballo Vogal
- Jesús Manuel Domínguez Gómez Vogal
Tipo: Tese
Resumo
In this memory there are used techniques of the theory of the Ordered Algebraic Structures, Duality in Locally Convex Lattices and Locally m-Convex Algebras, to give partial solutions to the classical problem of characterizing C(X), the space of real continuous functions on a completamente regularly space X. Concretely there are obtained characterizations of Ck (X) (C (X) endowed withe the compact convergence topology) as a Locally m-Convex algebra in two particular cases: for X a realcompact Kr-space and for X normal. Taking into account that, when X is realcompact, the compact convergence topology on C (X) coincides with its order topology, the previous algebraic-topological characterications have allowed, in particular, to contribute with tho new partial solutions to he problem of the algebraic characterization of C (X): for X a realcompact kr-space and for X normal and realcompact