A NEW TYPE OF REGULARITY IN FUZZY MINIMAL SPACE

This paper deals with a new type of open-like set in fuzzy minimal space [2], viz., fuzzy $m$-$\alpha$-preopen set taking fuzzy $m$-$\alpha$-open set [3] as a basic tool. Afterwards, we introduce an idempotent operator, viz., fuzzy $m$-$\alpha$-preclosure operator. With the help of this operator we introduce and study two new types of functions, viz., fuzzy $(m, m_{1})$-$\alpha$-precontinuous function and fuzzy $(m, m_{1})$-$\alpha$-preirresolute function. It is shown that fuzzy $(m, m_{1})$-$\alpha$-preirresolute function implies fuzzy $(m, m_{1})$-$\alpha$-precontinuous function, but reverse implication is not necessarily true, in general. Moreover, we introduce fuzzy $m$-$\alpha$-preregular space in which the reverse implication holds.