Definition:Ordinal Space/Closed/Uncountable

Definition
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.

Also see

 * Definition:Uncountable Open Ordinal Space


 * Definition:Countable Closed Ordinal Space
 * Definition:Countable Open Ordinal Space