The coreflective hull of $$\mathcal {U}$$-Fréchet spaces

Abstract

It is known that the category of all sequential spaces is a coreflective subcategory of the category of all topological spaces, and the coreflective hull of the category of all Frechet spaces is the category of all sequential spaces. In this paper, we generalize these results to $$\mathcal {U}$$ -sequential spaces and $$\mathcal {U}$$ -Frechet spaces where $$\mathcal {U}$$ is a free ultrafilter on $$\mathbb {N}$$ . Also we prove that the category of $$\mathcal {U}$$ -sequential spaces is a bi-coreflective subcategory of the category of all topological spaces where $$\mathcal {U}$$ is a free filter. As a consequence of these results, we get that some bi-coreflective subcategories of Top can be constructed by using free filters or free ultrafilters on $$\mathbb {N}$$ .