Abstract
An L-fuzzy topological space is said to be suitable if it possesses a nontrivial crisp closed subset. Basic properties of and sufficient conditions for suitable spaces are derived. Characterizations of the suitable subspaces of the fuzzy unit interval, the fuzzy open unit interval, and the fuzzy real line are obtained. Suitability is L-fuzzy productive; nondegenerate 1 ∗-Hausdorff spaces are suitable; the fuzzy unit interval, the fuzzy open unit interval, and the fuzzy real line are not suitable; and no suitable subspace of the fuzzy unit interval, the fuzzy open unit interval, or the fuzzy real line is a fuzzy retract of the fuzzy unit interval, the fuzzy open unit interval, or the fuzzy real line, respectively. Without restrictions there cannot be a fuzzy extension theorem.
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