A NEW TYPE OF REGULARITY IN FUZZY MINIMAL SPACE
Print ISSN: 2319-1023 | Online ISSN: 2582-5461 | Total Downloads : 9
DOI: https://doi.org/10.56827/JRSMMS.2024.1102.6
Author :
Anjana Bhattacharyya (Department of Mathematics, Victoria Institution (College), 78 B, A.P.C. Road, Kolkata - 700009, INDIA)
Abstract
This paper deals with a new type of open-like set in fuzzy minimal space [2], viz., fuzzy $m$-$\alpha$-preopen set taking fuzzy $m$-$\alpha$-open set [3] as a basic tool. Afterwards, we introduce an idempotent operator, viz., fuzzy $m$-$\alpha$-preclosure operator. With the help of this operator we introduce and study two new types of functions, viz., fuzzy $(m, m_{1})$-$\alpha$-precontinuous function and fuzzy $(m, m_{1})$-$\alpha$-preirresolute function. It is shown that fuzzy $(m, m_{1})$-$\alpha$-preirresolute function implies fuzzy $(m, m_{1})$-$\alpha$-precontinuous function, but reverse implication is not necessarily true, in general. Moreover, we introduce fuzzy $m$-$\alpha$-preregular space in which the reverse implication holds.
Keywords and Phrases
Fuzzy $m$-open set, fuzzy $m$-$\alpha$-preopen set, fuzzy $(m, m_{1})$-$\alpha$-precontinuous function, fuzzy $(m, m_{1})$-$\alpha$-preirresolute function, fuzzy $m$-$\alpha$- preregular space.
A.M.S. subject classification
54A40, 03E72.
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