Localic real functions: A general setting

DOI10.1016/j.jpaa.2008.11.004zbMath1187.06005OpenAlexW2144555319MaRDI QIDQ1008755

Tomasz Kubiak, Javier Gutiérrez García, Jorge Picado

Publication date: 30 March 2009

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10316/10042

zbMATH Keywords

continuitysemicontinuityframeframe of realspointfree topologyreal-valued functionslattice of sublocalesring of real-valued functions

Mathematics Subject Classification ID

Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable (26A15) Frames, locales (06D22) Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.) (54D15)

Related Items (24)

Normal semicontinuity and the Dedekind completion of pointfree function rings ⋮ Unnamed Item ⋮ Observables on \(\sigma\)-frame effect algebras as upper semicontinuous functions ⋮ Perfect locales and localic real functions ⋮ On the parallel between normality and extremal disconnectedness ⋮ Frame presentations of compact hedgehogs and their properties ⋮ Measurable functions on \(\sigma\)-frames ⋮ On the universal completion of pointfree function spaces ⋮ A point-free approach to canonical extensions of Boolean algebras and bounded Archimedean \(\ell \)-algebras ⋮ Extended real functions in pointfree topology ⋮ A general insertion theorem for uniform locales ⋮ Rings of real functions in pointfree topology ⋮ Hedgehog frames and a cardinal extension of normality ⋮ A note on middle \(P\)-spaces and related rings ⋮ A lattice-theoretic approach to arbitrary real functions on frames ⋮ General insertion and extension theorems for localic real functions ⋮ Insertion of continuous real functions on spaces, bispaces, ordered spaces and pointfree spaces -- a common root ⋮ Continuous extensions of real functions on arbitrary sublocales and \(C\)-, \(C^\ast\)-, and \(z\)-embeddings ⋮ More on locales in which every open sublocale is \(z\)-embedded ⋮ Insertion theorems for countably paracompact frames and stratifiable frames ⋮ Completely normal frames and real-valued functions ⋮ A unified view of the Dedekind completion of pointfree function rings ⋮ A Boolean extension of a frame and a representation of discontinuity ⋮ On classes of localic maps defined by their behavior on zero sublocales

Cites Work

• Stone-Čech compactification of locales. II
• Insertion of lattice-valued and hedgehog-valued functions
• On the algebraic representation of semicontinuity
• Pointfree forms of Dowker's and Michael's insertion theorems
• Monotone insertion and monotone extension of frame homomorphisms
• A new look at localic interpolation theorems
• Stone-Čech compactification of a product
• The Normal Completion of the Lattice of Continuous Functions
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