All Questions

Let $P = (V, \sqsubseteq)$ be a partial order and $\mathfrak{D}(P)$ denote the class of downward-closed subsets of the partial order $P$ (i.e, the class of $A \subseteq V$ such that $y\in A \;\&\; ...

Let $X$ be a directed-complete partial order, or even a complete lattice. A subset $S\subseteq X$ is called Scott-closed if and only if it is: Downward-closed: $y\in S$ and $x\le y$ implies $x\in S$; ...