w-C_0

Definition

• A topological space (X,τ) is said to be w-C_0 if .

Remark

• kernelを参照。

Property

• A topological space (X,τ) is w-C_0 iff for each x in X, there exists a proper closed set C such that x in C, i.e. iff for each x in X, cl({x}) ≠ X.
• If a space X is w-C_0, then for every topological space Y, the product space X×Y is also w-C_0.
• If a product X×Y is w-C_0, the at least one of the factor is w-C_0.

Reference

• Di Maio, Giuseppe, A separation axiom weaker than R0. (English) [J] Indian J. Pure Appl. Math. 16, 373-375 (1985).