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Tietze’s extension theorem in fuzzy topological spaces. (English) Zbl 0724.54006

Summary: This paper discusses the conceptual difficulties of generalizing standard topological terms to L-fuzzy topological terms. In particular, a theory of relative topologies and relative functions for L-fuzzy topological spaces is developed. The extension of a relative L-fuzzy continuous function into the fuzzy unit interval is defined. The equivalence of L- fuzzy continuous functions and monotone families of open sets is proved, and this equivalence is exploited to establish a fuzzy version of Tietze’s Extension Theorem. Finally, a partial converse to the theorem is proved.

MSC:

54A40 Fuzzy topology
54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.)
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References:

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