Definition:Clopen Set

Definition
Let $T$ be a topological space.

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

Then $S$ is described as clopen.

From Open and Closed Sets in a Topological Space, we have that in any topological space $T$, both $T$ and $\varnothing$ are clopen in $T$.

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.