Resumen de Functional ideals and topological theories

Robert Lowen, Tom Vroegrijk, Christophe Van Olmen

• 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