strong T_0

Definition

• A topological space (X,τ) is said to be strong T_0 if for each point x of X, the derived set {x}' is a finite union of a family of closed sets such that the intersection of non-empty members of the family is empty and at least one of the non-empty members is compact.

Property

• A normal strong T_0 ⇒ T_4?

Reference

• Singal, Asha Rani, Remarks on separation axioms. (English) [A] General Topology Relations modern Analysis Algebra, Proc. Kanpur topol. Conf. 1968, 265-296 (1971).