R*_0

Definition

• A topological space (X,τ) is said to be R*_0 if for every x∈X, either {x}' is the union of closed sets or {x}' does not contain a non-empty closed sed.

Property

• R*_0 + T_R = T_0.

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.