Abstract

This paper deals with a new type of fuzzy open-like set, viz., fuzzy pre $\beta$-open set, the class of which is strictly larger than that of fuzzy preopen set [7]. Using fuzzy pre $\beta$-open set as a basic tool, here we introduce fuzzy pre $\beta$-regular space in which fuzzy open set and fuzzy pre $\beta$-open set coincide. Here we introduce two new types of functions, viz., fuzzy pre $\beta$-continuous function, fuzzy pre $\beta$-irresolute function. The applications of these two functions on fuzzy pre $\beta$-regular space are discussed here.

Keywords and Phrases

Fuzzy $\beta$-open set, fuzzy pre $\beta$-open set, fuzzy pre $\beta$-regular space, fuzzy pre $\beta$-continuous function, fuzzy pre $\beta$-irresolute function, fuzzy almost compact space.

A.M.S. subject classification

54A40, 03E72.

.....