Filomat 2022 Volume 36, Issue 4, Pages: 1143-1157
https://doi.org/10.2298/FIL2204143A
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Two families of separation axioms on infra soft topological spaces
Al-Shami Tareq M. (Department of Mathematics, Sanaá University, Sanaá, Yemen), tareqalshami83@gmail.com
Mhemdi Abdelwaheb (Department of Mathematics, College of Sciences and Humanities in Aflaj Prince Sattam bin Abdulaziz University, Riyadh, Saudi Arabia), mhdiabd@gmail.com
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 Tj and infra pt-soft Tj-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.
Keywords: Partial belong relation, partial non-belong relation, total non-belong relation, soft separation axioms, extended infra soft topology
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