Continuity in partially ordered sets
type: Item
instance of: scholarly article
title: Continuity in partially ordered sets
zbMATH Open document ID: 1152.06004
DOI: 10.1155/2008/321761
author: Venu G. Menon
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2008-08-19T00:00:00Z
full work available at URL: https://eudml.org/doc/54856
review text: The author studies posets which need not be (directed) complete partial orders or lattices but which satisfy the condition that each element is the sup of elements way below it. He shows that some properties that are known to hold for cpos do hold for a more general kind of a partially ordered set. The following special case of a poset is central for this paper. A partially ordered set \(P\) is called a \(C\)-poset if, for any \(x,y\in P\), with \(x\not\leq y\), there exist a \(u\) such that \(u\not\leq y\) and an up-complete lower set \(J\) such that \(x\notin J\) and \(\uparrow u \cup J = P\). Probably, the author could have invented a more memorable name for his poset.
reviewed by: Vladimir Komendantsky
Mathematics Subject Classification ID: 06B35
zbMATH DE Number: 5313265
zbMATH Keywords: directed complete partial orders
zbMATH Keywords: continuous functions
zbMATH Keywords: non-complete partial orders
Wikidata QID: Q58645454
MaRDI profile type: Publication
OpenAlex ID: W2045931665
cites work: Continuous Lattices and Domains
cites work: On continuous noncomplete lattices.
description: scientific article; zbMATH DE number 5313265