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Fuzzy P-sets and fuzzy P'-sets in fuzzy topological spaces
G. Thangaraj,S. Muruganantham 원광대학교 기초자연과학연구소 2022 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.24 No.1
In this paper, the notions of fuzzy P-sets and fuzzy P'-sets in fuzzy topological spaces are introduced and several characterizations of these sets are established. A condition for the existence of fuzzy σ-nowhere dense sets in fuzzy hyperconnected spaces is obtained by means of fuzzy P-sets. The conditions under which fuzzy co-σ-boundary sets and fuzzy closed sets in fuzzy perfectly disconnected spaces become fuzzy P'-sets are established. A condition for fuzzy closed Fσ-sets in fuzzy F'-spaces to become fuzzy P'-sets is also obtained in this paper.
G. Thangaraj,S. Muruganantham 원광대학교 기초자연과학연구소 2023 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.25 No.2
In this paper, the concept of fuzzy F-spaces is introduced and studied. Several characterizations of fuzzy F-spaces are established. It is established that fuzzy F- spaces in which fuzzy $G_{\delta}$-sets are fuzzy open, are fuzzy normal spaces and fuzzy F-spaces in which fuzzy $G_{\delta}$- sets are fuzzy closed, are fuzzy F$'$-spaces. It is established that fuzzy F-spaces are not fuzzy hyperconnected spaces. A condition for fuzzy F$'$-spaces to become fuzzy F-spaces is obtained. The conditions under which fuzzy globally disconnected spaces and fuzzy perfectly disconnected spaces become fuzzy F-spaces are also obtained.