Definition:Clopen Set

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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

  • Results about clopen sets can be found here.

Linguistic Note

The term clopen set is a neologism which, in general, has no meaning outside the specialized language of topology.

However, in societies which the retail industry has a reputation for exploiting its workers, clopen is used in the context of the same person performing a closing shift followed by the opening shift the following day.