 \subset \mathsf{U}_{\hbox{\tiny $\mathrm{rec}$}}\mathbb{H} \times \mathsf{U}_{\hbox{\tiny $\mathrm{rec}$}}\mathbb{H}.\end{aligned}$$ Compactness of $\mathsf{U}_{\hbox{\tiny $\mathrm{rec}$}}\Sigma$ implies that $\math