Quasicontinuity of posets via Scott topology and sobrification
type: Item
instance of: scholarly article
title: Quasicontinuity of posets via Scott topology and sobrification
zbMATH Open document ID: 1124.06002
author: Xuxin Mao
author: Luoshan Xu
published in: Order
publication date: 2007-04-26T00:00:00Z
review text: The authors introduce and study quasicontinuous posets that are not directed complete and generalize various known results from domain theory to this context. For example, standard results about quasicontinuous dcpos are generalized to quasicontinuous posets, e.g., a poset is quasicontinuous if and only if its lattice of Scott open sets is hypercontinuous and a quasicontinuous poset is meet-continuous if and only if it is a continuous poset. By way of generalization from the theory of continuous posets, it is also shown that the directed completion of a quasicontinuous poset is again quasicontinuous and equipped with the Scott topology is the sobrification of the Scott topology of the original poset. A slightly more general version of the last result was obtained by the reviewer [Topology Appl. 21, 73--76 (1985; Zbl 0575.54013)].
Mathematics Subject Classification ID: 06B35
zbMATH DE Number: 5146180
zbMATH Keywords: quasicontinuous poset
zbMATH Keywords: meet-continuous poset
zbMATH Keywords: Scott topology
zbMATH Keywords: directed completion
zbMATH Keywords: sobrification
reviewed by: Jimmie D. Lawson
MaRDI profile type: Publication
full work available at URL: s11083-007-9054-4
OpenAlex ID: W2089371506
cites work: Q4693062
cites work: Generalized continuous and hypercontinuous lattices
cites work: Q3310666
cites work: Continuous Lattices and Domains
cites work: Q3864573
cites work: Q4500940
cites work: Posets having continuous intervals
cites work: Continuity of posets via Scott topology and sobrification
cites work: Q4472786
DOI: 10.1007/S11083-007-9054-4
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description: scientific article; zbMATH DE number 5146180