Definition:Clopen Set

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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.


Sources