R_{UD}

Definition

• A topological space (X,τ) is called an R_{UD}-space if for all x in X, cl{x} ∩ ker(x) = {x} ⇒ {x}' is the union of disjoint closed sets.

Property

• R_{UD} + T_0 = T_{UD}.

Reference

• Misra, D. N.; Dube, K. K., Some axioms weaker than the R0-axiom., (Serbo-Croatian summary), Glasnik Mat. Ser. III 8(28) (1973), 145-148.