# 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.

## Also known as

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

## Also see

• Results about clopen sets can be found here.

## Linguistic Note

The term clopen set is an obvious neologism which has no meaning outside the specialized language of topology.