Function spaces in metrically generated theoriesFunction spaces in metrically generated theories
Faculty of Sciences. Mathematics and Computer Science
Analytical and topological structures
Topology and its applications. - Amsterdam
156(2009):12, p. 2088-2100
University of Antwerp
The theory of metrically generated constructs provides us with an excellent setting for the study of function spaces. In this paper we develop a function space theory for metrically generated constructs and, by considering different metrically generated constructs, we capture interesting examples. For instance, for uniform spaces we retrieve the uniformity of uniform convergence and its generalization to Sigma-convergence and for UG-spaces we obtain a quantified version of these structures. Our theory also allows for many applications, in particular we are able to characterize the complete subspaces of these function spaces and we succeed in producing an appropriate Ascoli theorem. (C) 2009 Elsevier B.V. All rights reserved.