FTS0: The epireflective hull of the Sierpinski object in FTS

Abstract

In the category TOP of topological spaces, the epireflective hull of the standard two-point Sierpinski space is known to coincide with the subcategory of T0 topological spaces. In this note, we determine the epireflective hulls of the recently found 'Sierpinski objects' in the categories FTS, FNS and ω(TOP) of, respectively, fuzzy topological spaces, fuzzy neighborhood spaces and topologically generated fuzzy topological spaces. We thereby identify the corresponding 'T0-objects' in these categories and note that the categories FTS, FNS and ω(TOP) are 'universal'. © 1989.