Two types of separation axioms on supra soft topological spaces

In 2011, Shabir and Naz [1] employed the notion of soft sets to introduce the concept of soft topologies; and in 2014, El-Sheikh and Abd El-Latif [2] relaxed the conditions of soft topologies to construct a wider and more general class, namely supra soft topologies. In this disquisition, we continue studying supra soft topologies by presenting two kinds of supra soft separation axioms, namely supra soft -spaces and supra p-soft -spaces for = 0, 1, 2, 3, 4. These two types are formulated with respect to the ordinary points; and the difference between them is attributed to the applied non belong relations in their definitions.We investigate the relationships between them and their parametric supra topologies; and we provide many examples to separately elucidate the relationships among spaces of each type. Then we elaborate that supra p-soft -spaces are finer than supra soft -spaces in the case of = 0, 1, 4; and we demonstrate that supra soft -spaces are finer than supra p-soft -spaces.We point out that supra p-soft -axioms imply supra p-soft , however, this characterization does not hold for supra soft -axioms (see, Remark (3.30)). Also, we give a complete description of the concepts of supra p-soft -spaces ( = 1, 2) and supra p-soft regular spaces. Moreover,we define the finite product of supra soft spaces and manifest that the finite product of supra soft (supra p-soft ) is supra soft (supra p-soft ) for = 0, 1, 2, 3. After investigating some properties of these axioms in relation with some of the supra soft topological notions such as supra soft subspaces and enriched supra soft topologies, we explore the images of these axioms under soft -continuous mappings. Ultimately, we provide an illustrative diagram to show the interrelations between the initiated supra soft spaces.