Separation axioms and the fuzzy real lines
Fuzzy Sets and Systems
A categorical accommodation of various notions of fuzzy topology
Fuzzy Sets and Systems
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Let X be an L-fuzzy topological space. For @a @e L-1 and A @? X, x @ec"@a(A) if and only if G fuzzy-open and G(x) @a imply there is a @e A with G(a) 0. Under certain restrictions on @a, which are always satisfied if L is linearly ordered, c"@a is a semi-closure operator. This paper contains necessary and sufficient conditions under which a collection of semi-closure operators generates a fuzzy topology. In general, such a collection does not generate a unique topology. The class of topologies generated is shown to be closed under suprema and its largest member is characterized. The topology for the fuzzy unit interval is characterized among those generated by its @a-closure operators.