Soft α-separation axioms and α-fixed soft points

Soft set theory is a theme of interest for many authors working in various areas because of its rich potential for applications in many directions. it received the attention of the topologists who always seeking to generalize and apply the topological notions on different structures. To contribute to this research area, in this paper, we formulate new soft separation axioms, namely tt-soft alpha T-i (i = 0, 1, 2, 3, 4) and tt-soft alpha-regular spaces. They are defined using total belong and total non-belong relations with respect to ordinary points. This way of definition helps us to generalize existing comparable properties via general topology and to remove a strict condition of the shape of soft open and closed subsets of soft alpha-regular spaces. With the help of examples, we show the relationships between them as well as with soft alpha T-i (i = 0, 1, 2, 3, 4) and soft alpha-regular spaces. Also, we explore under what conditions they are kept between soft topological space and its parametric topological spaces. We characterize tt-soft alpha T-i and tt-soft alpha-regular spaces and give some conditions that guarantee the equivalence of tt-soft alpha T-i (i = 0, 1, 2) and the equivalence of tt-soft alpha T-i (i = 1, 2, 3). Further, we investigate some interrelations of them and some soft topological notions such as soft compactness, product soft spaces and sum of soft topological spaces. In the end, we study the main properties of of alpha-fixed soft point theorem.