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APPLICATIONS OF fπg-CLOSED SETS IN FUZZY TOPOLOGICAL SPACES


ANJANA BHATTACHARYYA
Victoria Institution (College), Department of Mathematics, 78B, A.P.C. Road, Kolkata-700009, INDIA e-mail: anjanabhattacharyya@hotmail.com

Issue:

SSRSMI, Number 1, Volume XXXII

Section:

Volume 32, Number 1

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.

Keywords:

Fuzzy π-open set, fπg-closed set, fuzzy regular open set, fuzzy semiopen set, fπg-continuous function, fπg-closed function, fπg-closure operator, fπg-irresolute function, fuzzy R-open function, fTπ-space.

Code [ID]:

SSRSMI202201V32S01A0002 [0005517]

Note:

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