Sequentially Compact Space is Countably Compact

Theorem
A sequentially compact topological space is also countably compact.

Proof
Let $T = \left({X, \tau}\right)$ be a sequentially compact topological space.

By definition of countably compact space, it suffices to show that every infinite sequence in $X$ has an accumulation point in $X$.

By the definition of a sequentially compact space, every infinite sequence in $X$ has a subsequence which converges in $X$.

The result follows from Limit Point of Sequence is Accumulation Point.