γ-βT_{1/2}

Definition

• A topological space (X,τ) with an operation γ on τ is called γ-βT_{1/2} if every γ-βg-closed set is γ-β-closed.

Property

• A topological space (X,τ) with an operation γ on τ is γ-βT_{1/2} if and only if each singleton {x} of X is either γ-β-closed or γ-β-open.
• Every topological space (X,τ) with an operation γ on τ is γ-βT_{1/2}.

Reference

• Basu, C. K.; Afsan, B. M. Uzzal; Ghosh, M. K., A class of functions and separation axioms with respect to an operation. (English summary), Hacet. J. Math. Stat. 38 (2009), no. 2, 103–118.