C_0

Definition

• A topological space (X,τ) is said to be C_0 if for every x∈X, {x}' is not union of non-empty closed sets.

Property

• C_0 + T_0 = T_1.
• C_0 ⇒ R_D.
• C_0 ⇒ T_1∨(∖T_{UD})?.

Reference

• 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.