Compactness is not box product-closed

Statement
It is possible to have a collection $$X_i, i \in I$$ of topological spaces, each of which is a compact space, but such that the product $$\prod_{i \in I} X_i$$, is not a compact space under the box topology.

Related facts

 * Compactness is product-closed under the product topology. For finite products, this can be even more easily proved using the tube lemma