A LEVEL-TOPOLOGIES CRITERION FOR LOWEN FUZZY UNIFORMIZABILITY

We study some relationships between a fuzzy uniformity and its alpha-l evel uniformities. We prove that a fuzzy neighbourhood space is fuzzy uniformizable iff its alpha-level spaces, for all 0 < alpha < 1, are u niformizable. We supply an explicit formula for a fuzzy uniformity ind ucing such a space. Similar criteria are established for the axioms of N-normality NT2, NT1, WNT1, NT0, WNT0 and NR0. We show that the two n otions of the alpha level uniformity of a fuzzy uniformity induced by a fuzzy metric, and the uniformity generated by the a-level metric of that fuzzy metric, are compatible. We also supply an explicit formula for a fuzzy pseudo-metric which induces a fuzzy neighbourhood space wh ose alpha-level topologies are pseudo-metrizable for all 0 < alpha < 1 .