Separation and Epimorphisms in Quasi-Uniform Spaces

Dikran Dikranjan () and Hans-Peter Künzi ()
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Dikran Dikranjan: Università di Udine, Dipartimento di Matematica e Informatica
Hans-Peter Künzi: University of Bern, Department of Mathematics

A chapter in Papers in Honour of Bernhard Banaschewski, 2000, pp 175-207 from Springer

Abstract: Abstract We study some categorical aspects of quasi-uniform spaces (mainly separation and epimorphisms) via closure operators in the sense of Dikranjan, Giuli, and Tholen. In order to exploit better the corresponding properties known for topological spaces we describe the behaviour of closure operators under the lifting along the forgetful functor T from quasi-uniform spaces to topological spaces. By means of appropriate closure operators we compute the epimorphisms of many categories of quasi-uniform spaces defined by means of separation axioms and study the preservation (reflection) of epimorphisms under the functor T.

Keywords: quasi-uniform space; uniform space; (regular semiregular) closure operator; θ-closure; sequential closure; S(α)-space; ϱ-separated space; epimorphism.; Primary 18A20; 54E15; 54B30; Secondary 18B30; 54B17 (search for similar items in EconPapers)
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-017-2529-3_10

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DOI: 10.1007/978-94-017-2529-3_10

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