5 problems

Is it true that for every co-sober topological space $X,$ the Hoare power space $\PH(X)$ is co-sober? In particular, does this hold when $X$ is $T_2$ or metrizab…

Let $P$ be a nonempty continuous dcpo, equipped with its Scott topology. Determine whether, without assuming that $P$ is bicomplete, the following classifications hold: (1) the Isb…

Let $X$ and $L$ be continuous domains, and let $T$ denote the domain used in the Scott function spaces $[X\to T]$ and $[T\to L]$. The paper considers finite-layer truncation maps a…

Let $\Xi$ be the universe of categories enriched in pointed DCPOs and Scott-continuous functors between them, respecting finite coproducts and initial objects. Let $\Theta$ be the…

Continuous-semantics conjecture. All the effective models living in the continuous semantics have non-r.e. equational theories.