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Generalized mappings between fuzzy topological spaces. (English) Zbl 0781.54006

Summary: In a previous paper [Ann. Soc. Sci. Brux., Sér. I 105, No. 4, 167-188 (1991; Zbl 0761.54003)] we introduced and studied the concept of \(\varphi\)-operation on a fuzzy topology \(\tau\) on a set \(X\). In this paper we introduce the concept of fuzzy \(\varphi\psi\)-continuous mappings which generalizes most forms of fuzzy continuity. Also we introduce the concept of fuzzy \(\varphi\psi\)-open (fuzzy \(\varphi\psi\)-closed) mappings in which fuzzy open (fuzzy closed) and fuzzy homeomorphism, fuzzy \(\theta\)-open (fuzzy \(\theta\)-closed) and fuzzy \(\delta\)-open (fuzzy \(\delta\)-closed) become special cases. Then we introduce the concept of fuzzy \(\varphi\psi\)-homeomorphism, generalizing the concepts of fuzzy homeomorphism, fuzzy \(\theta\)-homeomorphism and fuzzy \(\delta\)- homeomorphism. Finally, we prove that these concepts are good extensions.

MSC:

54A40 Fuzzy topology
54C08 Weak and generalized continuity

Citations:

Zbl 0761.54003
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