Clopen Set

In topology, a clopen set (a portmanteau of closed-open set) in a topological space is a set which is both open and closed. That this is possible for a set is not as counter-intuitive as it might seem if the terms open and closed were taken by their colloquial meaning as antonyms; mathematically, they are not antonyms. A set is defined to be closed if its complement is open, which leaves the possibility of an open set whose complement is itself also open, making the first set both open and closed, and therefore clopen.