Definition:Clopen Set

Definition
Let $T = \left({S, \tau}\right)$ 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.

Linguistic Note
The word clopen is an obvious neologism which has no meaning outside the specialized language of topology.

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 $T = \left({S, \tau}\right)$, both $S$ and $\varnothing$ are clopen in $T$.