On spaces with the property (wa)

[EN] A space X has the property (wa) (or is a space with the property (wa)) if for every open cover U of X and every dense subspace D of X, there exists a discrete subspace F C D such that St(F, U) = X. In this paper, we give an example of a Tychonoff space without the property (wa), and also study topological properties of spaces with the property (wa) by using the example.