# Category:Definitions/Ordinal Spaces

This category contains definitions related to Ordinal Spaces.
Related results can be found in Category:Ordinal Spaces.

Let $\Gamma$ be a limit ordinal.

### Open Ordinal Space

The open ordinal space on $\Gamma$ is the set $\hointr 0 \Gamma$ of all ordinal numbers (strictly) less than $\Gamma$, together with the order topology.

### Closed Ordinal Space

The closed ordinal space on $\Gamma$ is the set $\closedint 0 \Gamma$ of all ordinal numbers less than or equal to $\Gamma$, together with the order topology.

## Pages in category "Definitions/Ordinal Spaces"

The following 13 pages are in this category, out of 13 total.