New soft separation axioms and fixed soft points with respect to total belong and total non-belong relations

Abstract

In this article, we exploit the relations of total belong and total non-belong to introduce new soft separation axioms with respect to ordinary points, namely tttt-soft pre Ti(i=0,1,2,3,4){T}_{i}\hspace{0.33em}\left(i=0,1,2,3,4) and tttt-soft pre-regular spaces. The motivations to use these relations are, first, cancel the constant shape of soft pre-open and pre-closed subsets of soft pre-regular spaces, and second, generalization of existing comparable properties on classical topology. With the help of examples, we show the relationships between them as well as with soft pre Ti(i=0,1,2,3,4){T}_{i}\hspace{0.33em}\left(i=0,1,2,3,4) and soft pre-regular spaces. Also, we explain the role of soft hyperconnected and extended soft topological spaces in obtaining some interesting results. We characterize a tttt-soft pre-regular space and demonstrate that it guarantees the equivalence of tttt-soft pre Ti(i=0,1,2){T}_{i}\hspace{0.33em}\left(i=0,1,2). Furthermore, we investigate the behaviors of these soft separation axioms with the concepts of product and sum of soft spaces. Finally, we introduce a concept of pre-fixed soft point and study its main properties.

Keywords

• soft pre-open set
• tt-soft pre ti -space
• extended soft topology
• soft hyperconnected space
• additive property
• topological property
• soft pre-compact space
• pre-fixed soft point
• 47h10
• 54a05
• 54c15
• 54d10
• 54d15