*(English)*Zbl 0983.54024

For a space $(X,\tau )$, a function $U:X\to \tau $ such that each $x\in U\left(x\right)$ is called an open neighborhood assignment (ONA). $(X,\tau )$ is a $D$-space if for each ONA, $U$, there exists a closed discrete $D\subset X$ such that $\bigcup \left\{U\right(x)\mid x\in D\}=U\left(D\right)=X$. For an ONA $U:x\to \tau $ and $D\subset X$, $D$ is said to be $U$-sticky if $D$ is closed discrete and $x\in U\left(D\right)$ whenever $U\left(x\right)\cap D\ne \varnothing $. Among other results, it is proved that

(1) Box products of scattered spaces of height 1 are $D$-spaces,

(2) A subspace of a linearly ordered space is a $D$-space iff it has no closed stationary subset (a harder proof of this result is due to van Douwen),

(3) A subspace of the product of finitely many ordinals is a $D$-space iff it is metacompact iff it has no closed stationary subsets.