Abstract: | In [8], fuzzy π-closed sets are introduced. Using this concept as a basic tool, in [9] the notion of fuzzy π generalized closed set (fπg-closed set, for short) is introduced and stud-ied. Afterwards, a new type of generalized version of fuzzy closure operator, viz., fπg-closure operator is introduced which is an idempotent operator. Next we introduce a new type of generalized version of fuzzy open and closed-like functions, viz., fπg-open and fπg-closed functions and we characterize these two functions by using fπg-closure operator. Next we introduce fπg-continuous function and fπg-irresolute function. Then we introduce two new types of separation axioms, viz., fπg-regularity, fπg-normality and a new type of compactness, viz., fπg-compactness. It is shown that under fπg-irresolute function, fπg-regularity, fπg-normality and fπg-compactness remain invari-ant. Lastly, a new of fuzzy T2-space, viz., fπg-T2 space is introduced and it is shown that inverse image of fuzzy T2-space [20] (resp., fπg-T2 space) under fπg-continuous (resp., fπg-irresolute) function is an fπg-T2 space. |
