@bouncepaw Oh.
Also, oops, was wrong about the kinds of sets it uses:
en.wikipedia.org/wiki/Borel_se

Apparently it uses open or closed sets, which are like open or closed intervals. I supposed the reason they are interchangeable in the definition is that using set difference or union it's easy to convert between closed and open sets.

And using countably infinite operations is similar to thinking about infinite sums in analysis.