1. The problem statement, all variables and given/known data Let [itex]X[/itex] be a metric space, and [itex]A[/itex] its nonempty proper subset. Then is [itex]\partial A[/itex] not open? If it is, how do I prove it? Could you give me just some hints, not the whole solution? 2. Relevant equations 3. The attempt at a solution I cannot even start..