Document Type : Research Paper
Authors
- Pankaj Chettri ^{} ^{}
- Bishal Bhandari ^{}
Department of Mathematics, Sikkim Manipal Institute of Technology, Sikkim Manipal University Majitar, Rangpoo East Sikkim, India.
Abstract
The prime goal of this article is to initiate the notion of fuzzy $\mu^*$-open(closed) sets and fuzzy $\mu^*$-continuous functions and characterize them. These concepts are defined in a fuzzy topological space in presence of a generalized fuzzy topology, which becomes a new tool to study fuzzy topological spaces. It is observed that this class of fuzzy sets fail to form a fuzzy topology but it form a generalized fuzzy topology. Furthermore, the relationship of these fuzzy sets and fuzzy continuity with some existing fuzzy notions are established. Also the notion of fuzzy $(\tau, \mu^*)$-open(closed) functions is introduced and their equivalent conditions with fuzzy $\mu^*$-continuous functions are established.
Keywords
- Generalized fuzzy topology
- Fuzzy $\mu^*$-open (closed) set
- Fuzzy $\mu^*$-continuous function
- Fuzzy $(\tau
- \mu^*)$-closed (open) function
Main Subjects
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