A Comprehensive Review of the Coreflective Hull of T0​-Fuzzy Spaces

Abstract

The construction of the coreflective hull of ????0-fuzzy topological spaces has attracted increased interest from various authors, either as a tool or as a class of spaces to study and characterise its role in the structure of the category T0-????????????????, whose objects are fuzzy ????0-topological spaces and morphisms are fuzzy continuous maps (Sibahle Nxumalo, 2019). Moreover, the class of coreflective spaces in the classical category ????????????, whose objects are topological spaces and morphisms are continuous maps, has attracted considerable attention (Sibahle Nxumalo, 2019). It is well known that the coreflective hull of the class of ????0-topological spaces coincides with the class of ????2-spaces (Hausdorff spaces). Consequently, the construction of a fuzzy ????2-space on a given fuzzy ????0-space could play a crucial role in the study of the more general coreflective hull of fuzzy ????0-topological spaces. With the aim of obtaining such a construction, we further advance the study of fuzzy ????0-spaces to the more general fuzzy ????0-spaces.

Keywords: Coreflective Hull, Fuzzy ????0-Topological Spaces, Fuzzy Continuous Maps, Hausdorff Spaces (????2-Spaces), Category Theory in Topology.