Some New Types of Fuzzy Closed Sets, SeparationAxioms, and Compactness via Double Fuzzy Topologies
DOI:
https://doi.org/10.29020/nybg.ejpam.v17i4.5573Keywords:
intuitionistic fuzzy set, double fuzzy topology, (r, s)-gfsc set, (r,s)-g*fsc set, continuity, (r,s)-GFS-regular space, (r,s)-GFS-normal space, compactnessAbstract
In this article, we first defined a stronger form of (r,s)-generalized fuzzy semi-closed sets (briefly, (r,s)-gfsc sets) called (r,s)-g*fsc sets and investigated some of its features. Moreover, we showed that (r,s)-fsc set → (r,s)-g*fsc set → (r,s)-gfsc set, but the converse may not be true. In addition, we explored novel types of fuzzy generalized mappings between double fuzzy topological spaces (U, τ, τ*) and (V, η, η*), and the relationships between these classes of mappings were examined with the help of some illustrative examples. Thereafter, we introduced novel types of higher separation axioms called (r,s)-GFS-regular and (r,s)-GFS-normal spaces with the help of (r,s)-gfsc sets and discussed some topological properties of them. Finally, some novel types of compactness via (r,s)-gfso sets were defined and the relationships between them were introduced.
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Copyright (c) 2024 Fahad Alsharari, Osama Taha, Islam Taha
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