Bounded complete models of topological spaces
type: Item
instance of: scholarly article
title: Bounded complete models of topological spaces
zbMATH Open document ID: 1054.06004
author: Ralph Kopperman
author: Paweł Waszkiewicz
author: Hans Peter Künzi
published in: Topology and its Applications
publication date: 2004-08-19T00:00:00Z
review text: This paper provides a positive solution to a question of the reviewer and generalizes earlier related results by establishing that a metrizable space is completely metrizable if and only if it can be embedded as the set of maximal points of a bounded complete continuous domain (equipped with the relative Scott topology). The proof establishes and then exploits a generalization of the fact that a completely metrizable space \((X,\tau)\) admits a compact \(T_1\)-topology \(\tau^*\subseteq \tau\) such that the bitopological space \((X,\tau,\tau^*)\) is completely regular.
Mathematics Subject Classification ID: 06B35
Mathematics Subject Classification ID: 54C25
Mathematics Subject Classification ID: 54D35
Mathematics Subject Classification ID: 06F30
Mathematics Subject Classification ID: 68Q10
zbMATH DE Number: 2092805
zbMATH Keywords: domain theory
zbMATH Keywords: bounded complete domain
zbMATH Keywords: metric space
zbMATH Keywords: dcpo
zbMATH Keywords: quasiuniformity
zbMATH Keywords: quasiproximity
zbMATH Keywords: bitopological space
reviewed by: Jimmie D. Lawson
MaRDI profile type: Publication
full work available at URL: j.topol.2003.12.001
OpenAlex ID: W1971960701
cites work: Cotopology for metrizable spacees
cites work: Q4843177
cites work: Q4261083
cites work: Polish spaces, computable approximations, and bitopological spaces
cites work: Dynamical systems, measures, and fractals via domain theory
cites work: Q4231884
cites work: Continuity spaces: Reconciling domains and metric spaces
cites work: C-complete quasi-uniform spaces
cites work: Q3898534
cites work: Total objects of domains
cites work: All Topologies Come From Generalized Metrics
cites work: Asymmetry and duality in topology
cites work: Cocompactness and quasi-uniformizability of completely metrizable spaces.
cites work: Spaces of maximal points
cites work: Q4500940
cites work: The space of maximal elements in a compact domain
cites work: Topological games in domain theory
cites work: Effectively given domains
DOI: 10.1016/J.TOPOL.2003.12.001
description: scientific article; zbMATH DE number 2092805