Gr\"atzer-Hofmann-Lawson-Jung-S\"underhauf Duality

Abstract

We unify several extensions of the classic Stone duality due to Gr\"atzer, Hoffman-Lawson and Jung-S\"underhauf. Specifically we show that U-bases of locally compact sober spaces are dual to <-distributive v-predomains, where < is a transitive relation representing compact containment.