Weak Hausdorff separation axiom in I-fuzzy topological spaces and its application

In this paper, the weak Hausdorff separation axiom in the sense of Fang and Ren [A set of new separations axioms in L-fuzzy topological spaces, Fuzzy Sets and Systems 96 (1998) 359–376] is generalized from L-topologies to I-fuzzy topologies. It is shown that this notion satisfies the hereditary, productive properties, and the relations between it and other separation axioms are obtained. Also the degree to which an I-fuzzy topological space is weak Hausdorff is studied in terms of the fuzzy nets and the corresponding level I-topologies. As an application, we prove that the degree to which an I-fuzzy topological group is weak Hausdorff is equal to the degree to which it is T1.

► We generalized Fang–Ren-weak Hausdorff separation axiom from L-topologies to I-fuzzy topologies. ► Some properties of the weak Hausdorff separation axiom are studied. ► The relations between the weak Hausdorff separation axiom and other separation axioms are obtained. ► We prove that the degree to an I-fuzzy topological group is weak Hausdorff is equal to T1.