Abstract
We study some relationships between a fuzzy uniformity and its α-level uniformaties. We prove that a fuzzy neighbourhood space is fuzzy uniformizable iff its α-level spaces, for all 0< α<1, are uniformizable. We supply an explicit formula for a fuzzy uniformity inducing such a space. Similar criteria are established for the axioms of N-normality NT 2, NT 1, WNT 1, NT 0, WNT 0 and NR 0. We show that the two notions of the α-level uniformity of a fuzzy uniformity induced by a fuzzy metric, and the uniformity generated by the α-level metric of that fuzzy metric, are compatible. We also supply an explicit formula for a fuzzy pseudo-metric which induces a fuzzy neigbourhood space whose α-level topologies are pseudo-metrizable for all 0< α<1.
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