Strongly continuous posets and the local Scott topology
type: Item
instance of: scholarly article
title: Strongly continuous posets and the local Scott topology
zbMATH Open document ID: 1152.06005
author: Luoshan Xu
author: Xuxin Mao
published in: Journal of Mathematical Analysis and Applications
publication date: 2008-07-10T00:00:00Z
review text: The concept of a strongly continuous poset is defined. Four notions of continuity on posets are compared. The main results are: {\parindent=5mm \begin{itemize}\item[1)] A poset is strongly continuous iff its local Scott topology is equivalent to its Scott topology and is completely distributive iff it is a continuous precup. \item[2)] For precups, the four studied notions of continuity are equivalent, although they disagree on arbitrary posets. \item[3)] A \(T_0\)-space is a strongly continuous poset equipped with a Scott topology iff this space is weakly monotone convergent and has a distributive topology that is contained in the local Scott topology of the specialization order. \end{itemize}}
reviewed by: Vladimir Komendantsky
Mathematics Subject Classification ID: 06B35
zbMATH DE Number: 5299486
zbMATH Keywords: strongly continuous poset
zbMATH Keywords: weak monotone convergence space
zbMATH Keywords: specialization order
zbMATH Keywords: local Scott topology
zbMATH Keywords: principal ideal
MaRDI profile type: Publication
full work available at URL: j.jmaa.2008.04.067
OpenAlex ID: W1983777226
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DOI: 10.1016/J.JMAA.2008.04.067
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description: scientific article; zbMATH DE number 5299486