Lower Separation Axioms in 𝐂 ̌ech Fuzzy Soft Closure Spaces

Abstract

By considering 𝐶 ̌ech fuzzy soft closure spaces (𝑋,𝜃,𝐾), we provide a basic structure of a fuzzy soft topological space (𝑋,𝜏𝜃,𝐾) associated with 𝐶 ̌ech fuzzy soft closure space (𝑋,𝜃,𝐾). Separation axioms, namely, 𝑇𝑖 (𝑖 = 0,1,2), semi- (respectively, pseudo and Uryshon) 𝑇2 are studied in both 𝐶 ̌ech fuzzy soft closure spaces and its associative fuzzy soft topological spaces. It is shown that hereditary property is satisfied for 𝑇𝑖, 𝑖 = 0,1 with respect to 𝐶 ̌ech fuzzy soft closure space but for other mentioned types of separations axioms, hereditary property satisfies for closed subspaces of 𝐶 ̌ech fuzzy soft closure space. Several examples are given to illustrate each type of the separation axioms and to study the relationship between them.