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