*Definition [#ye691dde]
-A topological space (X,τ) is said to be R*_{UD} if for every x∈X, either {x}' is the union of disjoint closed sets or {x}' does not contain a non-empty closed sed.

*Property [#q14aa1b6]
-R*_{UD} + [[T_R]] = [[T_{UD}]].
-R*_{UD} ⇒ [[R*_0]].
-R*_{UD} ⇒ [[R_{UD}]].

*Reference [#tbcc6f82]
-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.