Countably Compact Space is Weakly Countably Compact

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

Proof
Let $T = \left({X, \vartheta}\right)$ be a countably compact space.

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

From Equivalent Definitions of Countably Compact, every infinite subset of $X$ has an $\omega$-accumulation point in $X$.

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

Hence the result.