If $E$ and $I$ are sets, we use $(E_i)_{i\in I}$ as a notation for a family of parts of $E$ indexed by $I$, i.e. an application $f:I\to \mathcal{P}(E)$, with $E_i:=f(i)$.
In the particular case where $I=\varnothing$, I am wondering if this notation holds (it exists a unique such application $g$, but how would we define $g(i)$ for $i\in\varnothing$...).
I am asking this question to well understand the answer of this post, which deals with a convention about the definition of covering spaces in Hatcher, Algebraic Topology. Thank you for your help !
The question was answered in the comments above.