1. The problem statement, all variables and given/known data Is it true that if U is an open set, then U = Int(closure(U))? 3. The attempt at a solution I feel like this may be true; I found counter-examples to the general form, Int(U)=(Int(closure(U)), but they all seem to hinge on U being not open (A subset of rationals in the reals, which is neither open nor closed). However I can't prove this one way or another; I'd like a nudging in the right direction of the proof is this is true, and just a, "it's false" if it's false, so I can keep hunting for a CE.