  For a countably infinite group $\Gamma$, let $\mathcal{W}_\Gamma$ denote the
space of all weak equivalence classes of measure-preserving actions of $\Gamma$
on atomless standard probability spaces, equipped with the compact metrizable
topology introduced by Ab\'{e}rt and Elek. There is a natural multiplication
operation on $\mathcal{W}_\Gamma$ (induced by taking products of actions) that
makes $\mathcal{W}_\Gamma$ an Abelian semigroup. Burton, Kechris, and Tamuz
showed that if $\Gamma$ is amenable, then $\mathcal{W}_\Gamma$ is a topological
semigroup, i.e., the product map $\mathcal{W}_\Gamma \times \mathcal{W}_\Gamma
\to \mathcal{W}_\Gamma \colon (\mathfrak{a}, \mathfrak{b}) \mapsto \mathfrak{a}
\times \mathfrak{b}$ is continuous. In contrast to that, we prove that if
$\Gamma$ is a Zariski dense subgroup of $\mathrm{SL}_d(\mathbb{Z})$ for some $d
\geqslant 2$ (for instance, if $\Gamma$ is a non-Abelian free group), then
multiplication on $\mathcal{W}_\Gamma$ is discontinuous, even when restricted
to the subspace $\mathcal{FW}_\Gamma$ of all free weak equivalence classes.
