Anjana Bhattacharyya, More On Fuzzy Regular Preopen Sets, Volume 2017, Number 1, Pages 9-22, 2017

# Anjana Bhattacharyya, More On Fuzzy Regular Preopen Sets, Volume 2017, Number 1, Pages 9-22, 2017

Abstract: In this paper we have first introduced fuzzy $p$-closed and fuzzy regular $p$-closed spaces and then characterized these two concepts in several ways. Afterwards, we have introduced two new concepts of fuzzy cover, viz., fuzzy $p$-cover and fuzzy regular $p$-cover respectively and characterized fuzzy $p$-closed and fuzzy regular $p$-closed spaces via these two new concepts of fuzzy cover. Also fuzzy $p$-closed space is characterized by fuzzy net. Again we have introduced fuzzy $p$-closed and fuzzy regular $p$-closed sets and characterized them in different ways, especially via prefilterbases. In the last section, three different types of fuzzy continuous-like functions, viz. fuzzy regular precontinuous, fuzzy strongly $\theta$-precontinuous and fuzzy $p$-continuous functions are introduced and some applications of these three functions are established.

Key words: Fuzzy regular $p$-closed set, fuzzy extremally disconnected space, fuzzy regular precontinuous function, fuzzy regular $p^{*}$-cluster point of prefilterbase.

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