Normal semicontinuity and the Dedekind completion of pointfree function rings

DOI10.1007/s00012-016-0378-zzbMath1353.06004OpenAlexW2189235550MaRDI QIDQ292834

Imanol Mozo Carollo, Jorge Picado, Javier Gutiérrez García

Publication date: 9 June 2016

Published in: Algebra Universalis (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10316/43797

zbMATH Keywords

localeframeBooleanizationcb-framecontinuous real functionDedekind completionextended real functionframe of extended realsframe of realsfunction ringGleason coverHausdorff continuous real functionnormal semicontinuous real functionpartial real functionpartial realsreal functionsublocale lattice

Mathematics Subject Classification ID

Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable (26A15) Complete lattices, completions (06B23) Frames, locales (06D22) Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.) (54D15) Real-valued functions in general topology (54C30) Ordered rings, algebras, modules (06F25) Ordered rings (13J25)

Related Items (5)

Pseudocompleteness in the category of locales ⋮ A point-free approach to canonical extensions of Boolean algebras and bounded Archimedean \(\ell \)-algebras ⋮ A lattice-theoretic approach to arbitrary real functions on frames ⋮ A unified view of the Dedekind completion of pointfree function rings ⋮ On the Menger and almost Menger properties in locales

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the parallel between normality and extremal disconnectedness
• Extended real functions in pointfree topology
• On the Dedekind completion of function rings.
• General insertion and extension theorems for localic real functions
• Rings of real functions in pointfree topology
• An algebraic view of weaker forms of realcompactness
• On the algebraic representation of semicontinuity
• Pointfree forms of Dowker's and Michael's insertion theorems
• Localic real functions: A general setting
• Lower and upper regularizations of frame semicontinuous real functions
• The Gleason cover of a topos. I
• Essential completeness in categories of completely regular frames.
• Realcompactness and certain types of subframes
• The Dedekind completion of \(C({\mathcal X})\)
• The normal completion of a subset of a complete lattice and lattices of continuous functions
• The Dedekind completion ofC(X): an interval-valued functions approach
• Frames and Locales
• Lattice-ordered Rings and Modules
• Dedekind Order Completion ofC(X) by Hausdorff Continuous Functions
• The Completion of an Archimedean f -Ring
• On a Class of Countably Paracompact Spaces
• Boundedness Properties in Function-Lattices
• The Normal Completion of the Lattice of Continuous Functions
• Über das System aller stetigen Funktionen auf einem topologischen Raum

This page was built for publication: Normal semicontinuity and the Dedekind completion of pointfree function rings