Definition:Ordinal Space/Open/Countable

Definition
Let $\Gamma$ be a limit ordinal.

Let $\Omega$ denote the first uncountable ordinal.

The countable open ordinal space on $\Gamma$ is a particular case of an open ordinal space $\left[{0 \,.\,.\, \Gamma}\right)$ where $\Gamma < \Omega$.

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

Also see

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


 * Definition:Countable Closed Ordinal Space