Which one is more correct?$V_y$ or $V_i$

Question

In the theorem $26.3 $: every compact subspace of a hausdorff space is closed

Munkre say that the collection $\{V_y|y \in Y\}$ is a covering of $Y$ by sets open in $X$

But many authors write $ \{V_i\}_{i \in I }$ is an open cover of $Y$

Here im confused about Munkres style of writing .

$Y$ is not an index set .$Y$ is a compact subspace of the hausdorff space $X $

So i think Munkres style of writing is wrong.He should write like this $\{V_y|y \in I\}$ .

I am confused in regards to these two writing $\{V_y|y \in Y\}$ and $ \{V_i\}_{i \in I }$ Which one is more correct?