1. The problem statement, all variables and given/known data I started studying point-set topology a while ago, and I started to wonder, "Does a set have to be partially ordered in order to define a topology on it?" 2. Relevant equations 3. The attempt at a solution I know that every set in a topology has to be open, which means that at any point you can construct an open ball such that every point in the open ball is also in that set. I don't see how this would work unless there was some sort of relation like <, >, or something similar on the set. Perhaps I'm not seeing the generalization to sets other than R^n, but I'm at a complete loss.