\begin{definition}[Definition:Ordinal Space/Closed]
Let $\Gamma$ be a limit ordinal.
The '''closed ordinal space on $\Gamma$''' is the set $\closedint 0 \Gamma$ 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:
\end{definition}