Find a counterexample of:
the union of the closure of A_i = the closure of the union of A_i
I hope its understandable
I was trying to come up with a conterexample in using the definition I posed above (same idea) but I used finite number of sets. And I forgot the important rule of analysis (or topology here): what works for finite sets does not necessarily work for infinite sets.
So I am guessing if was such that then the above would actually be true. Correct? Maybe this is consequence of Heine-Borel theorem, no?