*Definition [#lde210c0]
-A topological space is said to be T_D if for every point x of X, &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5c%7bx%5c%7d'%20%5c%5d%7d%25.png); (the [[derived set]] of {x}) is a closed set.

*Property [#af7cdf39]
-T_D = [[T_0]] + [[R_D]]. [2]
-T_D = [[T_R]] + [[R*_D]]. [3]
-T_D ⇒ [[T_{UD}]].


*Reference [#s29ef75a]
+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, ''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.