Function spaces in metrically generated theories |
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Authors: | E Vandersmissen A Van Geenhoven |
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Institution: | a Vrije Universiteit Brussel, Vakgroep Wiskunde, Pleinlaan 2, 1050 Brussel, Belgium b Universiteit Antwerpen, Middelheimlaan 1, 2020 Antwerpen, Belgium |
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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 Σ-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. |
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Keywords: | 18B99 54B30 54C35 54D99 |
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