T_D

Definition

• A topological space is said to be T_D if for every point x of X, (the derived set of {x}) is a closed set.

Property

• T_D = T_0 + R_D. [2]
• T_D = T_R + R*_D. [3]
• T_D ⇒ T_{UD}.

Reference

1. Aull, Charles E.; Thron, W.J.,Separation axioms between T0 and T1., (English) [J] Nederl. Akad. Wet., Proc., Ser. A 65, 26-37 (1962).
2. 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.
3. 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.