γ-βT_1

Definition

• A topological space (X,τ) with an operation γ on τ is called γ-βT_1 if and only if for each pair of distinct points x, y in X, there exists two γ-β-open sets U and V such that x ∈ U, and y ∈ V.

Property

• A topological space (X,τ) with an operation γ on τ is γ-βT_1 if and only if every singleton {x} is γ-β-closed.
• γ-βT_1 ⇒ 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.