weakly countably compact LimitPointCompact 2002-01-04 19:04:04 2007-05-28 03:22:20 Definition limit point compactness weak countable compactness topology A topological space $X$ is said to be \emph{weakly countably compact} (or \emph{limit point compact}) if every infinite subset of $X$ has a limit point. Every countably compact space is weakly countably compact. The converse is true in \PMlinkname{$\mathrm{T}_1$ spaces}{T1Space}. A metric space is weakly countably compact if and only if it is compact. An easy example of a space $X$ that is not weakly countably compact is any infinite set with the discrete topology. A more interesting example is the countable complement topology on an uncountable set.