Research Article

Supported approach spaces

Published in: Quaestiones Mathematicae
Volume 46 , issue S1 : SPECIAL ISSUE DEDICATED TO THE MEMORY OF PROFESSOR HORST HERRLICH , 2023 , pages: 161–190

DOI: 10.2989/16073606.2023.2247724

Author(s): E. Colebunders Vrije Universiteit Brussel, België , R. Lowen Universiteit Antwerpen, België

Keywords: 54A05 , 54C05 , 54C10 , 54D30 , 54E35 , 54E40 , 54E99 , Approach space , uniform approach space , quasi-metric coreflection , topological coreflection , contraction , closed and open expansiveness , compactness , regularity , weak adjointness , supported , split

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Abstract

In this paper we work in the category of approach spaces with contractions [14], the objects of which are sets endowed with a numerical distance between sets and points. Approach spaces are to be considered a simultaneous generalization of both quasi-metric and topological spaces. Especially the fundamental notion of distance is reminiscent of the closure operator in a topological space and of the point-to-set distance in a quasi-metric space.

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