Definition:Ordinal Space/Open

Definition
Let $\Gamma$ be a limit ordinal.

The open ordinal space on $\Gamma$ is the set $\left[{0 \,.\,.\, \Gamma}\right)$ of all ordinal numbers (strictly) less than $\Gamma$, together with the order topology.

Particular special cases of an open ordinal space are as follows:

Also see

 * Definition:Closed Ordinal Space