In the present paper, we introduce and discuss a new set of separation properties in fuzzy soft topological spaces called $ FS\delta $-separation and $ FS\delta $-regularity axioms by using fuzzy soft $ \delta $-open sets and the quasi-coincident relation. We provide a comprehensive study of their properties with some supporting examples. Our analysis includes more characterizations, results, and theorems related to these notions, which contributes to a deeper understanding of fuzzy soft separability properties. We show that the $ FS\delta $-separation and $ FS\delta $-regularity axioms are harmonic and heredity property. Additionally, we examine the connections between $ FS{\delta }^* $-compactness and $ FS\delta $-separation axioms and explore the relationships between them. Overall, this work offers a new perspective on the theory of separation properties in fuzzy soft topological spaces, as well as provides a robust foundation for further research in the transmission of properties from fuzzy soft topologies to fuzzy and soft topologies and vice-versa by swapping between the membership function and characteristic function in the case of fuzzy topology and the set of parameters and a singleton set in the case of soft topology.
Citation: Tareq M. Al-shami, Salem Saleh, Alaa M. Abd El-latif, Abdelwaheb Mhemdi. Novel categories of spaces in the frame of fuzzy soft topologies[J]. AIMS Mathematics, 2024, 9(3): 6305-6320. doi: 10.3934/math.2024307
In the present paper, we introduce and discuss a new set of separation properties in fuzzy soft topological spaces called $ FS\delta $-separation and $ FS\delta $-regularity axioms by using fuzzy soft $ \delta $-open sets and the quasi-coincident relation. We provide a comprehensive study of their properties with some supporting examples. Our analysis includes more characterizations, results, and theorems related to these notions, which contributes to a deeper understanding of fuzzy soft separability properties. We show that the $ FS\delta $-separation and $ FS\delta $-regularity axioms are harmonic and heredity property. Additionally, we examine the connections between $ FS{\delta }^* $-compactness and $ FS\delta $-separation axioms and explore the relationships between them. Overall, this work offers a new perspective on the theory of separation properties in fuzzy soft topological spaces, as well as provides a robust foundation for further research in the transmission of properties from fuzzy soft topologies to fuzzy and soft topologies and vice-versa by swapping between the membership function and characteristic function in the case of fuzzy topology and the set of parameters and a singleton set in the case of soft topology.
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