# Definition:Ordinal Space

## Definition

The ordinal spaces are classified as follows:

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.

## Also see

• Results about ordinal spaces can be found here.