A Hofmann-Mislove theorem for bitopological spaces
type: Item
instance of: scholarly article
title: A Hofmann-Mislove theorem for bitopological spaces
zbMATH Open document ID: 1221.54036
author: Achim Jung
author: M. Andrew Moshier
published in: The Journal of Logic and Algebraic Programming
publication date: 2008-09-01T00:00:00Z
review text: A `frame' is a complete lattice in which finite meets distribute over arbitrary joins. A frame homomorphism preserves finite meets and arbitrary joins leading to the category Frm. There is a dual adjunction between Top and Frm. With the duality between topological spaces and frames the authors have presented a Stone duality for bitopological spaces. In the process, the concept of \(d\)-frame has been introduced; with necessary accessories, the resulting category is denoted by \(d\)Frm; for a bitopological space the authors have taken two topologies \(\tau_+\) and \(\tau_-\) with no connection between them; morphisms between bitopological spaces are required to be continuous with respect to each of the topologies and finally, with all these, the category biTop is generated; the authors have proved a dual adjunction between biTop and \(d\)Frm. Under the additional assumption of regularity, the authors have proved a characterization theorem for subsets of a bisober space that are compact in one and closed in the other topology. This is an analogue to the celebrated Hofmann-Mislove theorem for sober spaces.
Mathematics Subject Classification ID: 54E55
Mathematics Subject Classification ID: 06D22
Mathematics Subject Classification ID: 68N17
Mathematics Subject Classification ID: 68Q55
zbMATH DE Number: 5318668
zbMATH Keywords: bitopological spaces
zbMATH Keywords: d-frames
zbMATH Keywords: stone duality
zbMATH Keywords: sober spaces
zbMATH Keywords: Hofmann-Mislove theorem
MaRDI profile type: Publication
full work available at URL: j.jlap.2008.02.007
OpenAlex ID: W1963658540
cites work: Domain theory in logical form
cites work: Q4843177
cites work: BIFRAMES AND BISPACES
cites work: Q3858244
cites work: Q3360172
cites work: A ternary operation in distributive lattices
cites work: Q4530231
cites work: Synthetic topology: of data types and classical spaces
cites work: Continuous Lattices and Domains
cites work: Q3915037
cites work: Q3965241
cites work: Q3997287
cites work: A Hofmann-Mislove theorem for Bitopological Spaces
cites work: A Direct Proof of the Hofmann-Mislove Theorem
cites work: Q3864573
cites work: Q3920613
cites work: Q3316563
cites work: Q4525542
cites work: Q3994458
DOI: 10.1016/J.JLAP.2008.02.007
description: scientific article; zbMATH DE number 5318668