Coreflections Versus Regular Epimorphisms in Categories of Topological Spaces

Author: inura J.

Source: Applied Categorical Structures, Volume 6, Number 4, December 1998 , pp. 527-530(4)

Publisher: Springer

Abstract:

Let {\cal A} be an epireflective subcategory of the category Top of topological spaces which is not contained in the category of indiscrete spaces (e.g. Top, the category of Hausdorff spaces, the category of Tychonoff spaces) and {\cal B} be a coreflective subcategory of {\cal A}. In this paper we prove that the coreflector{\cal A}\to {\cal B} preserves regular epimorphisms if and only if {\cal B}={\cal A} or {\cal B} is contained in the category of discrete spaces.

Keywords: coreflective subcategory; epireflective subcategory; regular epimorphism; ultraspace

Language: English

Document Type: Regular paper

Affiliations: 1: Faculty of Mathematics and Physics, Comenius University, Mlynská dolina, 842 15 Bratislava, Slovak Republic. E-mail: Email: cincura@fmph.uniba.sk

Publication date: 1998-12-01

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