nearly T_3

Definition

• A topological space (X,τ) is said to be nearly T_3 space if for each point x in X and an open neighbourhood V of x there exists a T_3-open cover U of (X, τ) such taht , where is star of the point x with respect to U.

Property

• nearly T_3 ⇒ T(3,1) ⇒ T(3,2) ⇒ T(3,3).
• nearly T_3 ⇒ nearly T_2.

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.