The Priestley duality for \(\prec \)-distributive \(\vee \)-predomains

Abstract

In this paper, we present a Priestley-type topological representation for \(\prec \)-distributive \(\vee \)-predomains, thereby answering an open problem posed by T. Bice. Moreover, we establish a dual equivalence between the category of \(\prec \)-distributive \(\vee \)-predomains with \(\prec \)-morphisms and that of DP-compact pospaces with DP-morphisms. In particular, our results restrict to Hansoul-Poussart duality for bounded distributive sup-semilattices and to a Priestley duality for continuous frames.