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GENERALIZED VERSION OF FUZZY δ-SEMICLOSED SET


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 XXVIII

Section:

Volume 28, Number 1

Abstract:

The notions of fuzzy δ-semiopen and fuzzy δ-semiclosed set have been introduced in [5]. Taking this idea as a basic tool, we introduce the notion of fuzzy generalized δ-semiclosed set (fgδ-semiclosed set, for short). Then the mutual relationships between this set with fg-closed set [2, 3], fgs-closed set [3], fsg-closed set [3], fgβ-closed set [3], fβg-closed set [3] are established. Afterwards, we introduce and characterize fgδ-semiclosed function. In Section 4, a new type of idempotent operator, viz., generalized δ-semiclosure operator is introduced and studied some of its properties. Next we introduce and characterize fuzzy generalized δ-semicontinuous function and show that the composition of two fuzzy generalized δ-semicontinuous functions may not be so. In Section 5, we introduce and characterize fuzzy generalized δ-semiregular and fuzzy generalized -δseminormal spaces and also we prove the invariance of the propery of a fuzzy topological space of being generalized δ-seminormal, under fuzzy generalized δ-semiirresolute function. In the last section, we first introduce fuzzy generalized δ-semi T2-space and then three different types of fuzzy continuous-like functions are introduced and establish that the inverse image of fuzzy generalized δ-semi T2-space under these functions are

fuzzy T2-spaces [13].

Keywords:

fgδ-semiclosed set, fgδ-semiclosed function, fgδ-semicontinuous function, fgδ-semiregular (normal) space, fgδ-semi T2-space.

Code [ID]:

SSRSMI201801V28S01A0001 [0004808]

Note:

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