A characterization of fuzzy compactifications (Q1823499)

The main theorem (3.2) attempts to give a characterization of the set of all ultra fuzzy compactifications for a fuzzy topological space. Unfortunately, the result is not correct. A simple counterexample is as follows: let X be real interval [0,1], \(\tilde F\) the usual topology, and F the set of characteristic maps of F. Let \(BX=X\cup \{y\}\), where y is a point and \(y\not\in X\), and define h: BX\(\to [0,1]\) by \(h(z)=\) when \(z\in X\) and \(h(y)=3/2\). The fuzzy topology on BX generated by \(F\cup \{h\}\) is denoted by H. Now it is easy to see that (X,F) itself is compact and is not dense in (BX,\(\iota\) (H)). Moreover, there exists no topology T on BX satisfying the requirement of the Theorem 3.2.