Product of Countably Compact Spaces is not always Countably Compact

Theorem
Let $I$ be an indexing set.

Let $\left\langle{\left({S_\alpha, \tau_\alpha}\right)}\right \rangle_{\alpha \mathop \in I}$ be a family of topological spaces indexed by $I$.

Let $\displaystyle \left({S, \tau}\right) = \prod_{\alpha \mathop \in I} \left({S_\alpha, \tau_\alpha}\right)$ be the product space of $\left\langle{\left({S_\alpha, \tau_\alpha}\right)}\right \rangle_{\alpha \mathop \in I}$.

Let each of $\left({S_\alpha, \tau_\alpha}\right)$ be countably compact.

Then it is not necessarily the case that $\left({S, \tau}\right)$ is also countably compact.

Proof
Let $T$ denote the Novak space.

Let $T \times T$ denote the Cartesian product of the Novak space with itself under the product topology.

From Novak Space is Countably Compact, $T$ is a countably compact space.

But from Cartesian Product of Novak Spaces is not Countably Compact, $T \times T$ is not a countably compact space.

Hence the result.