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.