A non-sober core-compact meet-continuous dcpo

Abstract

We construct a meet-continuous dcpo whose Scott space is core-compact but neither sober nor locally compact. The example is a proper sub-dcpo of a locally compact sober complete lattice, and restriction induces an isomorphism between their lattices of Scott-closed sets. It follows that a locally compact sober dcpo need not be determined, among all dcpos, by its Scott-closed-set lattice.