QFS-domains and quasicontinuous domains.
type: Item
instance of: scholarly article
title: QFS-domains and quasicontinuous domains.
zbMATH Open document ID: 1320.06006
author: Wenfeng Zhang
author: Xiaoquan Xu
publication date: 2015-07-23T00:00:00Z
review text: In domain theory difficulties with cartesian closedness are well-known, namely the category of continuous domains and Scott-continuous functions is not cartesian closed. Identifying maximal cartesian closed subcategories is a subtle matter which gave rise to the notions of RB-domains and FS-domains, and further to quasicontinuous domains, QRB-domains, and QFS-domains. In this article the notion of \(\omega\)QFS-domain is given, and in a short series of results it is shown that for a QFS-domain, \(\omega\)QFS is equivalent to the existence of a countable base for the Scott topology, that Scott-continuous retracts of QFS-domains are QFS-domains, that Lawson compactness for a quasicontinuous domain is determined by a certain condition on upper sets, and that QFS-domains are quasicontinuous domains together with a certain separating condition.
reviewed by: Ittay Weiss
Mathematics Subject Classification ID: 06B30
Mathematics Subject Classification ID: 06B35
Mathematics Subject Classification ID: 54D30
Mathematics Subject Classification ID: 54C15
zbMATH DE Number: 6463534
zbMATH Keywords: QFS-domains
zbMATH Keywords: quasicontinuous domains
zbMATH Keywords: Scott topology
zbMATH Keywords: Lawson compactness
MaRDI profile type: Publication
full work available at URL: s10114-015-3676-z
OpenAlex ID: W2028483377
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DOI: 10.1007/S10114-015-3676-Z
published in: Acta Mathematica Sinica, English Series
description: scientific article