On soft topological ordered spaces

Abstract

In this paper, the authors initiate a soft topological ordered space by adding a partial order relation to the structure of a soft topological space. Some concepts such as monotone soft sets and increasing (decreasing) soft operators are presented and their main properties are studied in detail. The notions of ordered soft separation axioms, namely p-soft Ti-ordered spaces (i=0,1,2,3,4) are introduced and the relationships among them are illustrated with the help of examples. In particular, the equivalent conditions for p-soft regularly ordered spaces and soft normally ordered spaces are given. Moreover, we define the soft topological ordered properties and then verify that the property of being p-soft Ti-ordered spaces is a soft topological ordered property, for i=0,1,2,3,4. Finally, we investigate the relationships between soft compactness and some ordered soft separation axioms and point out that the condition of soft compactness is sufficient for the equivalent between p-soft T2-ordered spaces and p-soft T3-ordered spaces.