Ideals of quasi-ordered sets.
type: Item
instance of: scholarly article
title: Ideals of quasi-ordered sets.
zbMATH Open document ID: 1058.06002
author: Elias David
published in: Algebra Universalis
publication date: 2005-04-19T00:00:00Z
review text: For a given collection of subsets \(\mathcal A\) of a quasi-ordered set or a poset \(Z\) the author defines the collection \(\mathcal I(\mathcal A)\) of \(\mathcal A\)-ideals of \(Z\). They form a closure system, and this leads to the definition of \(\mathcal A\)-ideal continuity of functions. The author shows the existence of a choice-free \(\mathcal A\)-ideal continuous imbedding of a poset into a \({\mathcal B}\)-join complete poset with an appropriate universal mapping property. Topological applications include the imbedding of Scott spaces and Alexandrov spaces into up-complete Scott spaces.
reviewed by: Radomír Halaš
Mathematics Subject Classification ID: 06A06
Mathematics Subject Classification ID: 06B35
zbMATH DE Number: 2158768
zbMATH Keywords: quasi-ordered set
zbMATH Keywords: \(\mathcal A\)-ideals
zbMATH Keywords: closure system
zbMATH Keywords: \(\mathcal A\)-ideal continuity
zbMATH Keywords: continuous imbedding
zbMATH Keywords: join complete poset
zbMATH Keywords: universal mapping property
zbMATH Keywords: Scott spaces
zbMATH Keywords: Alexandrov spaces
zbMATH Keywords: functor
MaRDI profile type: Publication
full work available at URL: s00012-002-8177-0
OpenAlex ID: W2015352186
DOI: 10.1007/S00012-002-8177-0
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description: scientific article; zbMATH DE number 2158768