\begin{definition}[Definition:Ordinal Space/Open]
Let $\Gamma$ be a limit ordinal.
The '''open ordinal space on $\Gamma$''' is the set $\hointr 0 \Gamma$ of all ordinal numbers (strictly) less than $\Gamma$, together with the order topology.
Particular special cases of an '''open ordinal space''' are as follows:
\end{definition}