Soft separation axioms via soft topological operators

Abstract

This paper begins with an introduction to some soft topological operators that will be used to characterize several soft separation axioms followed by their main properties. Then, we define a new soft separation axiom called "soft $ T_D $-space" and analyze its main properties. We also show that this space precisely lies between soft $ T_0 $ and soft $ T_1 $-spaces. Finally, we characterize soft $ T_i $-spaces, for $ i = 0, 1, D $, in terms of the stated operators.

Keywords

• soft topology
• soft operator
• soft shell
• soft kernel
• soft derived set
• soft t₀-space
• soft t₁-space
• soft t_d-space