Faithfulness of Directed Complete Posets based on Scott Closed Set Lattices

Dongsheng Zhao, Luoshan Xu

By Thron, a topological space $X$ has the property that $C(X)$ isomorphic to $C(Y)$ implies $X$ is homeomorphic to $Y$ iff $X$ is sober and $T_D$, where $C(X)$ and $C(Y)$ denote th…