nearly T_1

Definition

• A topological space (X,τ) is said to be nearly T_1 space if for each point x in X and an open neighbourhood V of x there exists a T_1-open cover U of (X, τ) such taht , where is star of the point x with respect to U.

Property

• nearly T_1 ⇒ T(1,1) ⇒ T(1,2) ⇒ T(1,3).

Reference

• Przemski, M., Nearly T_i-continuous functions and some separation axioms. (Serbo-Croatian summary), Glas. Mat. Ser. III 21(41) (1986), no. 2, 431–435.