MORE CHARACTERIZATIONS ABOUT SOFT SETS AND SOFT CONTINUITY

We introduce and study the indicator soft sets (Ind(A), P) where A ⊂ P and P is the set of parameters. We use the indicator soft sets to define the indicator soft topology Ind(τ) where τ is any topology on the set of parameters P. We show that τ and Ind(τ) have the same corresponding properties: compactness, Lindelöf property, second-countable, separation axioms. We proved that a soft mapping fpu: (U, Ind(τ), P) → (U^′, Ind(τ^′), P^′) is soft continuous (quasi-continuous, open, closed, soft homeomorphism) iff p: (P, τ) → (P^′, τ^′) is continuous (quasi-continuous, open, closed, homeomorphism). We use these results to generate counter examples for soft topological spaces. For example, we gave an example to show that soft quasi-continuous mapping are not soft continuous, another example to show that soft T₃ − space are not soft T₄, and an example to show that none of the soft separation axioms are preserved under soft open mappings.