Title
Function spaces in metrically generated theories Function spaces in metrically generated theories
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
Amsterdam ,
Subject
Mathematics
Source (journal)
Topology and its applications. - Amsterdam
Volume/pages
156(2009) :12 , p. 2088-2100
ISSN
0166-8641
ISI
000267388100012
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
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.
Full text (open access)
https://repository.uantwerpen.be/docman/irua/60fd1f/5627.pdf
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