Countably Compact Space is Weakly Countably Compact

Theorem
Every countably compact space is a weakly countably compact space.

Proof
Let $T = \struct {S, \tau}$ be a countably compact space.

By definition:
 * $T$ is weakly countably compact every infinite subset of $S$ has a limit point in $S$.

By definition of countably compact space:
 * every infinite subset of $S$ has an $\omega$-accumulation point in $S$.

By definition, an $\omega$-accumulation point is a limit point.

Hence the result.