Definition:Ordinal Space/Closed/Countable

Definition
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 $\left[{0 \,.\,.\, \Gamma}\right]$ where $\Gamma < \Omega$.

That is, it is the set $\left[{0 \,.\,.\, \Gamma}\right]$ of all ordinal numbers less than or equal to $\Gamma < \Omega$, together with the order topology.

Also see

 * Definition:Countable Open Ordinal Space


 * Definition:Uncountable Closed Ordinal Space
 * Definition:Uncountable Open Ordinal Space