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SUM OF SOFT TOPOLOGICAL ORDERED SPACES

This study aims to introduce the concept of sum of soft topological ordered spaces using pairwise disjoint soft topological ordered spaces and investigate its main properties. To link between soft topological spaces and their sum, we define ordered additive, finitely ordered additive and countably ordered additive properties. Then, we demonstrate that the properties of being p-soft Ti-ordered, soft Ti-ordered and strong soft Ti-ordered spaces are ordered additive and prove that the properties of monotonically soft compact and ordered soft compact spaces are finitely ordered additive. In this content, we study some features of soft λ-continuous, soft λ-open, soft λ-closed and soft λ-homeomorphism, where λ ∈ {I,D,B}. Finally, we give some examples and discuss under which conditions a soft topological ordered space represents the sum of some soft ordered topological spaces.