Limit point compact

In mathematics, a topological space ${\displaystyle X}$ is said to be limit point compact or weakly countably compact if every infinite subset of ${\displaystyle X}$ has a limit point in ${\displaystyle X.}$ This property generalizes a property of compact spaces. In a metric space, limit point compactness, compactness, and sequential compactness are all equivalent. For general topological spaces, however, these three notions of compactness are not equivalent.