1. The problem statement, all variables and given/known data Show that (0,1) is no homeomorphic to [0,1] 2. Relevant equations 3. The attempt at a solution I understand the usual procedure for proving this - remove a point from each of the spaces and check for connectedness. My only question is, the topology on each space isn't specified. Do I assume it's the subspace topology or what? In general, when given questions like this, with no topology given, do I just infer from the context of the question which topology I should use?