Tietze's extension theorem in fuzzy topological spaces
Authors:
Mary P. Reagor
David F. Addis
Affiliation:
Department of Mathematics, Weatherford College, Weatherford, TX 76086, U.S.A.
Department of Mathematics, Texas Christian University, Fort Worth, TX 76129, U.S.A.
Abstract:
This paper discusses the conceptual difficulties of generalizing standard topological terms of 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.