meaning of the notation $\mathcal{U}/V$

Question

If $\mathcal{U}$ is an open cover of a uniform space and $\mathcal{V}$ is a uniform cover then what is the meaning of the notation $\mathcal{U}/V$ where $V \in \mathcal{V}$?

Answer 1

The following definition is given on the first page of the paper.

If $u$ and $v$ are uniformities on the same set, then $u/v$ is the quasi- uniformity generated by covers of the form $\{V_s \cap U_t^s\}$, where $\{V_s\} \in v$, and for each $s$, $\mathcal{U}^s = \{U_t^s\} \in u$.

From this, it is reasonable to guess that if $\mathcal{U}$ is an open cover, $\mathcal{V}$ is a uniform cover and $V \in \mathcal{V}$, then $\mathcal{U}/V$ is the $V$-cover $\{V \cap U \mid U \in \mathcal{U}\}$. Would it make sense?