Corrigendum: A completion for partially ordered Abelian groups
It has come to my attention that the proof of Theorem 2.8 in my article [ibid. 28, 273-290 (1984; Zbl 0541.06011)] is not correct. It is claimed that if (\b{W},H) is a semicontinuous closed poset and if \(G\to^{f}H\) is a Scott continuous homomorphism of partially ordered abelian groups, then if \(w\in W\), the set \(\gamma (w)=\{a\in G|\) f(a)\(\leq w\}\) is Scott closed in G. This need not be true, if sups in H are not preserved when computed in \b{W}. The proof can be amended by changing the definition of semicontinuous closed poset as follows. A semicontinuous closed poset is a pair (\b{V},G) satisfying Definition 2.6 (pg. 284) together with the requirement that the inclusion \(G\hookrightarrow \underline V\) preserves directed sups. This additional assumption does not affect the primary example considered in the paper.
scientific article; zbMATH DE number 3898954