Let $X$ be a topological group and let $D$ is a countable discrete closed subset of $X$. We also let $ \mathcal U= \{U_d: d\in D\}$ of open sets of $X$ such that witnesses that $D$ is closed discrete, i.e., for every $d \in D$, $U_d \cap D=\{d\}$.
Is there a family $\mathcal W= \{W_d: d\in D\}$ of open sets of $X$ such that (1) $W_d\cap D=\{d\}$ for each $d\in D$; (2) $\overline{\bigcup W} \subset \bigcup \mathcal U$?
Thanks ahead.
It seems the following.
:-) At the first sight this question is not related to my speciality. But at the second... Let $G$ be a pseudocompact topological group which is not countably compact. I leave to you the pleasure to do the rest.