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Separation and Epimorphisms in Quasi-Uniform Spaces

In: Papers in Honour of Bernhard Banaschewski

Author

Listed:
  • Dikran Dikranjan

    (Università di Udine, Dipartimento di Matematica e Informatica)

  • Hans-Peter Künzi

    (University of Bern, Department of Mathematics)

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.

Suggested Citation

  • Dikran Dikranjan & Hans-Peter Künzi, 2000. "Separation and Epimorphisms in Quasi-Uniform Spaces," Springer Books, in: Guillaume Brümmer & Christopher Gilmour (ed.), Papers in Honour of Bernhard Banaschewski, pages 175-207, Springer.
    • Handle: RePEc:spr:sprchp:978-94-017-2529-3_10
    DOI: 10.1007/978-94-017-2529-3_10
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