weakly semi-R_0

Definition

• A topological space (X,τ) is said to be weakly semi-R_0 if .

Property

• A topological space X is weakly semi-R_0 if and only if s-ker(x)≠ X for any x∈X, where s-ker(x) is
  semi-kernel of x.
• Let f:X → Y be a pre-semi-closed one-one function. If X is weakly semi-R0, then so is Y.
• If a space X is weakly semi-R_0, then for every space Y, the product space X × Y is also weakly semi-R_0.

Reference

• Arya, S.P.; Nour, T.M., Weakly semi-R_0 spaces., (English) [J] Indian J. Pure Appl. Math. 21, No.12, 1083-1085 (1990).