Definition:Weakly Countably Compact Space

Definition

Let $T = \struct {S, \tau}$ be a topological space.

$T$ is weakly countably compact if and only if every infinite subset of $S$ has a limit point in $S$.

Also known as

A space which is weakly countably compact can also be described as limit point compact.

Also see

• Definition:Countably Compact Space

• Results about weakly countably compact spaces can be found here.

Sources

• 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $3$: Compactness: Global Compactness Properties