An Approach to Generate New Soft Sets and Spaces in Soft Ditopological Spaces

Abstract

In this paper, the detailed analysis of soft ditopological space theory (SDT - space theory) isameliorated by introducing new soft sets called  -b-open sets,  -b-closed sets and  -b-densesets, which are needed for the definition of extremally disconnected spaces and submaximalspaces in soft ditopological spaces. Moreover,  -regular- open,  -preopen,  -semi open,  --open and  -- open sets in SDT-space are defined and studied relations between these setsin detail. A new idea is introduced in order to prove relations, which gives an affirmativeanswer to understand the structure of SDT-spaces. It is proved that individually these systemscan still be quite complicated, a possibly more tractable task is to describe their possible jointdistributions by utilizing new defined  -sets.