# Category:Ordinal Spaces

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This category contains results about Ordinal Spaces.

Definitions specific to this category can be found in Definitions/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 "Ordinal Spaces"

The following 28 pages are in this category, out of 28 total.

### C

### O

### U

- Uncountable Closed Ordinal Space is Countably Compact
- Uncountable Closed Ordinal Space is Lindelöf
- Uncountable Closed Ordinal Space is not First-Countable
- Uncountable Closed Ordinal Space is not Perfectly Normal
- Uncountable Closed Ordinal Space is not Second-Countable
- Uncountable Closed Ordinal Space is not Separable
- Uncountable Closed Ordinal Space is Sigma-Compact
- Uncountable Open Ordinal Space is Countably Compact
- Uncountable Open Ordinal Space is First-Countable
- Uncountable Open Ordinal Space is not Lindelöf
- Uncountable Open Ordinal Space is not Metacompact
- Uncountable Open Ordinal Space is not Paracompact
- Uncountable Open Ordinal Space is not Second-Countable
- Uncountable Open Ordinal Space is not Separable
- Uncountable Open Ordinal Space is not Sigma-Compact
- Uncountable Open Ordinal Space is Sequentially Compact