### Clopen

Not to be confused with Half-open interval.

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 may seem counter-intuitive, as the common meanings of*open*and*closed*are antonyms. But their mathematical definitions are not mutually exclusive. A set is closed if its complement is open, which leaves the possibility of an open set whose complement is also open, making both sets both open*and*closed, and therefore clopen.
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