Soft α-separation axioms and α-fixed soft points

Abstract

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 αTi(i=0,1,2,3,4) and tt-soft α-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 α-regular spaces. With the help of examples, we show the relationships between them as well as with soft αTi(i=0,1,2,3,4) and soft α-regular spaces. Also, we explore under what conditions they are kept between soft topological space and its parametric topological spaces. We characterize tt-soft αT1 and tt-soft α-regular spaces and give some conditions that guarantee the equivalence of tt-soft αTi(i=0,1,2) and the equivalence of tt-soft αTi(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 α-fixed soft point theorem.

Keywords

• soft α-open set
• tt-soft αti-space (i=0
• 1
• 2
• 3
• 4)
• extended soft topology
• additive property
• topological property
• soft α-compact space
• α-fixed soft point