Two families of separation axioms on infra soft topological spaces

Tareq M Al-Shami, Abdelwaheb Mhemdi

Many generalizations of soft topology were studied in the literature; an infra soft topology is the recent one of these generalizations. In this paper, we put on view two classes of soft separation axioms in the frame of infra soft topologies, namely infra pp-soft T j and infra pt-soft T j-spaces (j = 0, 1, 2, 3, 4). Both of them are formulated with respect to distinct ordinary points such that the first class defined using partial belong and partial non-belong relations, and the second one defined using partial belong and total non-belong relations. Following systematic lines of this type of study, we first show the relationships between them with the aid of examples. We also establish main properties and explore their behaviour under some special types of infra soft topologies. Transmission of these classes between infra soft topology and its parametric infra topologies are amply studied. Moreover, we scrutinize their features in terms of hereditary and topological properties, and finite product of soft spaces.