New types of soft ordered mappings via soft α-open sets

Abstract

The concept of soft topological ordered spaces is an extension of the soft topological spaces notion.  The motivation of this paper is twofold: One is to generalize and extend the existing ordered maps and other is to contribute on making a general framework for studying soft topological ordered spaces.  In this study, we utilize soft α-open sets to introduce new ordered maps, which generalize existing comparable notions, namely soft xα-continuous, soft xα-open, soft xα-closed and soft xα-homeomorphism maps, for x ∈ {I, D, B}, via soft topological ordered spaces.  We show the relationships among these concepts and discuss the equivalent conditions for each one of them .  Also, we derive that an extended soft topologies notion guarantees the equivalent between the soft maps initiated herein and their counterparts of maps on topological ordered spaces.  For illustration and comparison, various examples are provided.