Definition:Clopen Set

Definition
Let $T = \struct {S, \tau}$ be a topological space.

Let $X \subseteq S$ such that $X$ is both open in $T$ and closed in $T$.

Then $X$ is described as clopen.

Also known as
Earlier sources refer to clopen sets as closed-open sets or open-closed sets.

Also see

 * Open and Closed Sets in Topological Space: in any topological space $T = \struct {S, \tau}$, both $S$ and $\O$ are clopen in $T$.