Definition:Ordinal Space/Closed

Definition
Let $\Gamma$ be a limit ordinal.

The closed ordinal space on $\Gamma$ is the set $\left[{0 \,.\,.\, \Gamma}\right]$ of all ordinal numbers less than or equal to $\Gamma$, together with the order topology.

Particular special cases of a closed ordinal space are as follows:

Also see

 * Definition:Open Ordinal Space