Abstract

We develop a theory of α-Hausdorff fuzzy topological spaces which is compatible with α-compactness and fuzzy continuity, and for α a certain type of member of a given lattice we obtain characterizations of the α-Hausdorff subspaces of the fuzzy unit interval, the fuzzy open unit interval, and the fuzzy real line. In route we give an easy proof of the Fuzzy Tychonov Theorem for α-compactness and extend the theory of one-point α-compactifications.

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