*Definition [#o08ff861]
-A topological space (X,τ) is said to be w-C_0 if &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5ccap_%7bx%5cin%20X%7d%5cker%28x%29=%5cemptyset%20%5c%5d%7d%25.png);.

*Remark [#m51d778b]
-[[kernel]]を参照。

*Property [#l72c074f]
-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 [#k146a1ac]
-Di Maio, Giuseppe, ''A separation axiom weaker than R0.'' (English) [J] Indian J. Pure Appl. Math. 16, 373-375 (1985).