3 problems

Let $\mathsf{Infosys}$ be the category of infosys, and consider the upper powerlocale on this category. A continuous meet semilattice is a continuous domain with finite meets. Vick…

Let $\mathsf{Infosys}$ be the category of infosys, let $\mathsf{ContLat}$ be the category of continuous lattices, and consider the monad on $\mathsf{Infosys}$ arising from the lowe…

Finite-set preservation conjecture. If $T$ restricts to finite sets, then the $T$-power construction preserves compactness.