COREFLECTIONS INDUCED BY FINE FUNCTORS

Abstract

In 1974 A. W. Hager initiated the study of metric-fine uniform spaces. It was observed that the definition of metric-fine spaces relied on the class M of metric uniform spaces and the fine functor α, which reequips every uniform space with its fine uniformity, in a rather categorical way. By substituting for M other suitable classes K and for α other suitable functors F, called fine functors here, an analogous process leads to K-F-fine spaces, which always form bicoreflective subcategories. In this paper we give a description of the associated bicoreflectors in the realm of arbitrary topological categories of H. Herrlich. As an illustration two classes of K-F-fine spaces in the category of nearness spaces are presented.