A set E in ℝ is nowhere dense if and only if the closure of E's complement(E with a line over it) is dense in ℝ
I need help proving this lemma. I'm not entirely sure where to start.
The Attempt at a Solution
I know we have to proof it two ways, backwards and forwards. For the forward, all I can think to use if the fact that the closure of E complement contains no nonempty open intervals, but I don't know where to go with that.
Any help would be appreciated.