\(FTS_ 0:\) The epireflective hull of the Sierpinski object in FTS (Q1111186)

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 \(T_ 0\) topological spaces. We determine the epireflective hulls of the recently found `Sierpinski objects' in the categories FTS, FNS and \(\omega\) (TOP) of, respectively, fuzzy topological spaces, fuzzy neighborhood spaces and topologically generated fuzzy topological spaces. We thereby identify the corresponding `\(T_ 0\)-objects' in these categories and note that the categories FTS, FNS and \(\omega\) (TOP) are `universal'.