*Definition [#jabc8fbb]
-A topological space (X,τ) is said to be T_{UD} if for every point x of X, {x}' is a union of disjoint closed set (where {x}' is the [[derived set]] of {x}).

*Property [#o60fae8f]

-A topological space (X,τ) is a T_{UD} space iff ∀x,y∈X, y∈{x}' and {x}' is not a union of disjoint closed sets implies &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5c%7by%5c%7d'=%5cemptyset%20%5c%5d%7d%25.png);. [3]
-T_{UD} = [[T_0]] + [[R_{UD}]]. [2]
-T_{UD} = [[T_R]] + [[R*_{UD}]]. [4]

*Reference [#x66cdf6f]
+Aull, Charles E.; Thron, W.J.,''Separation axioms between T0 and T1.'', (English) [J] Nederl. Akad. Wet., Proc., Ser. A 65, 26-37 (1962).
+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.
+Guia, Josep, ''Axioms weaker than R0.'', (Serbo-Croatian summary), Mat. Vesnik 36 (1984), no. 3, 195–205.
+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.