Limit point compact
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In general topology, a topological space X is said to be limit point compact or weakly countably compact if every infinite subset of X has a limit point.
Limit point compactness is equivalent to countable compactness if X is a T1-space and is equivalent to compactness if X is a metric space.
An easy example of a space X that is not weakly countably compact is any countable (or larger) set with the discrete topology. A more interesting example is the countable complement topology.
Every countably compact space is weakly countably compact, but the converse is not true.
- This article incorporates material from Limit point compact on PlanetMath, which is licensed under the GFDL.
- This article incorporates material from Weakly countably compact on PlanetMath, which is licensed under the GFDL.
