Definition:Ordinal Space/Open/Countable

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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 $\hointr 0 \Gamma$ where $\Gamma < \Omega$.

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

Also see

  • Results about ordinal spaces can be found here.