Category:Ordinal Spaces
Jump to navigation
Jump to search
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