\begin{definition}[Definition:Ordinal Space/Closed/Countable]
Let $\Gamma$ be a limit ordinal.
Let $\Omega$ denote the first uncountable ordinal.
The '''countable closed ordinal space on $\Gamma$''' is a particular case of an closed ordinal space $\closedint 0 \Gamma$ where $\Gamma < \Omega$.
That is, it is the set $\closedint 0 \Gamma$ of all ordinal numbers less than or equal to $\Gamma < \Omega$, together with the order topology.
\end{definition}