For example, if I want to write a closure of a set, which is denoted A_1, should I use $\overline{A_1}$ or $\overline A_1$ (or something completely different)?
For me, the more logical choice seems to be $\overline{A_1}$ (since I read \overline command as "closure of"). But maybe from typographical point of view this can be considered differently.
Here is a MathB.in link for comparison. (I am aware that rendering in MathJax and LaTeX is not necessarily the same, but I do not know what is standard way to make images with symbols for TeX.SE posts.)
Here is also a picture which I tried to create from pdf output using the method described in this answer on meta.

I have seen that there exists a question \overline and \widehat with subscript. But that question asks about subscript added to the bar symbol, not subscript added to the symbol(s) which are under the bar.
