Coreflections Versus Regular Epimorphisms in Categories of Topological Spaces

Let 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 be a coreflective subcategory of . In this paper we prove that the coreflector preserves regular epimorphisms if and only if or is contained in the category of discrete spaces.