Sobre la caracterización del álgebra topológica de las funciones reales y continuas sobre un espacio topológico

  1. Pulgarín García, Antonio Ángel
Dirigée par:
  1. Francisco Montalvo Durán Directeur/trice
  2. Batildo Requejo Fernández Directeur/trice

Université de défendre: Universidad de Extremadura

Fecha de defensa: 13 septembre 2003

Jury:
  1. José Luis Blasco Olcina President
  2. María Ángeles Mulero Díaz Secrétaire
  3. Manuel Sanchís López Rapporteur
  4. María Isabel Garrido Carballo Rapporteur
  5. Jesús Manuel Domínguez Gómez Rapporteur

Type: Thèses

Résumé

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