T_R

Definition

• A topological space (X,τ) is said to be T_R if for every x∈X, either {x}' is empty or {x}' contains a non-empty closed set.

Property

• A topological space (X,τ) is a T_R space iff any non-empty closed subset of X contains a closed singleton set.
• T_R + R_0 = T_1.

Reference

• Guia, Josep, Essentially T_D and essentially T_UD spaces., Bull. Math. Soc. Sci. Math. R. S. Roumanie (N.S.) 32(80) (1988), no. 3, 227-233.