Abstract

We investigate approximating posets with projections (approximating pop's). These are triples (D; ; P) consisting of a poset (D; ) and a directed set P of projections with sup P = id D . They carry a canonical uniformity and thus a topology. We relate their properties such as completeness and compactness to properties of the poset and the projection set. We show that each monotone net in D is convergent if and only if (D; ) is an algebraic domain such that the images of the projections are precisely the compact elements of (D; ). We call these domains P-domains and characterize them as inverse limits of posets satisfying the ascending chain condition. Moreover, we describe P-domains by a certain system of so-called "complete" subsets. We prove that if the set of compact elements of an algebraic domain is mub-complete, then it is a P-domain if and only if the mub-closure of every finite set of compact elements fulfils the ascending chain condition. Furthermore, we characte...

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