Corrigendum: A completion for partially ordered Abelian groups
type: Item
instance of: scholarly article
title: Corrigendum: A completion for partially ordered Abelian groups
zbMATH Open document ID: 0564.06009
DOI: 10.1007/BF02575528
author: K. I. Rosenthal
published in: Semigroup Forum
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/134655
review text: 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.
Mathematics Subject Classification ID: 06F20
Mathematics Subject Classification ID: 06B23
Mathematics Subject Classification ID: 06F30
Mathematics Subject Classification ID: 06A06
zbMATH DE Number: 3898954
zbMATH Keywords: semicontinuous closed poset
zbMATH Keywords: Scott continuous homomorphism
zbMATH Keywords: partially ordered abelian groups
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3898954