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