Functional ideals and topological theories

• Autores: Robert Lowen, Tom Vroegrijk, Christophe Van Olmen
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 34, Nº 4, 2008, págs. 1065-1090
• Idioma: inglés
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• Resumen

  • In this paper we give new and unified isomorphic characterizations of approach spaces, pre-approach spaces, convergence approach spaces, uniform gauge spaces, topological spaces, convergence spaces, pretopological spaces, metric spaces and uniform spaces. The unified treatment is made possible by the use of a type of ideals of positive real-valued functions, a concept, richer and more appropriate than filters for our purpose