A space $(X,\tau)$ is called a *$D$-space* if if whenever one is given a neighborhood $N(x)$ of $x$ for each $x\in X$, then there is a closed discrete subset $D\subseteq X$ such that $\{N(x): x\in D\}$ covers $X$. [This][1] is a survey of $D$-spaces and their properties.

A routine verification shows that whenever $X_i$ are $D$-spaces for all $i$, then so is $\prod_{i\in I}^{\textrm{Box}}X_{i}$.


  [1]: http://www.auburn.edu/~gruengf/papers/dsurv7.pdf