### An upper power domain construction in terms of strongly compact sets [chapter]

Reinhold Heckmann
1992 Lecture Notes in Computer Science
A novel upper power domain construction is de ned by means of strongly compact sets. Its power domains contain less elements than the classical ones in terms of compact sets, but still admit all necessary operations, i.e. they contain less junk. The notion of strong compactness allows a proof of stronger properties than compactness would, e.g. an intrinsic universal property of the upper power construction, and its commutation with the lower construction. B Y , f A] is the image of A and f ?1
more » ... the inverse image of B. Domains A poset (partially ordered set) is a set P together with a re exive, antisymmetric, and transitive relation' '. We often identify the poset P = (P; ) with its carrier P. For A P, let #A be the set of all points below some point of A, and correspondingly "A the set of all points above some point of A. Often, we abbreviate #fxg by #x and "fxg by "x. We refrain from doing so if x happens to be a set. A P is a lower set i #A = A, and an upper set i "A = A.