Why are families of sets sometimes denoted with $(-)$ instead of $\{ - \}$?

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Why are set families sometimes denoted with $(-)$ instead of $\{ - \}$?

In particular, I often see open covers of a topological space being notated as $(U_i)_{i \in I}$, or an arbitrary family of indexed sets notated as $(A_\lambda)_{\lambda \in \Lambda}$, for example.

I have always wondered, why the use of parenthesis instead of curly brackets?

Edit: For an example, see here, page 7. (this is just the most recent one, though I can't think of any other papers off-hand that use this notation, but I've definitely seen it a lot).