1. The problem statement, all variables and given/known data Prove that any open subset of [itex]\Real[/itex] can be written as an at most countable union of disjoint open intervals. 2. Relevant equations An at most countable set is either finite or infinitely countable. 3. The attempt at a solution It seems very intuitive but I am at lost where to even start. We're doing compactness in metric spaces so I would assume it must apply. But I thought a set has to be closed in order to be compact and this deals with an open subset so it can't possibly be compact. Any help would be much appreciated!