Countably compact space
From Wikipedia, the free encyclopedia
(Redirected from Countably compact)
- The first uncountable ordinal (with the order topology) is an example of a countably compact space that is not compact.
- A compact space is countably compact.
- A countably compact space is always limit point compact.
- For metrizable spaces, countable compactness, sequential compactness, limit point compactness and compactness are all equivalent.
- The example of the set of all real numbers with the standard topology shows that neither local compactness nor σ-compactness nor paracompactness imply countable compactness.
- For T1 spaces, countable compactness and limit point compactness are equivalent.
See also 
|This topology-related article is a stub. You can help Wikipedia by expanding it.|