Continuous extensions of real functions on arbitrary sublocales and \(C\)-, \(C^\ast\)-, and \(z\)-embeddings

DOI10.1016/j.jpaa.2021.106702zbMath1473.18014OpenAlexW3128776941MaRDI QIDQ2031562

Jorge Picado, Ana Belén Avilez

Publication date: 9 June 2021

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

Full work available at URL: https://doi.org/10.1016/j.jpaa.2021.106702

zbMATH Keywords

localeframecompletely separated sublocaleslocalic extension theorem\(C\)- and \(C^\ast\)-embedded sublocales\(z\)-embedded sublocale

Mathematics Subject Classification ID

Frames, locales (06D22) Extension of maps (54C20) (C)- and (C^*)-embedding (54C45) Real-valued functions in general topology (54C30) Frames and locales, pointfree topology, Stone duality (18F70)

Related Items (2)

Frame presentations of compact hedgehogs and their properties ⋮ On classes of localic maps defined by their behavior on zero sublocales

Cites Work

• General insertion and extension theorems for localic real functions
• Rings of real functions in pointfree topology
• Remainders in pointfree topology
• Localic real functions: A general setting
• Hedgehog frames and a cardinal extension of normality
• Coz-onto frame maps and some applications
• Frames and Locales
• C- and C^*-quotients in pointfree topology
• Cozero bases of frames
• Sublocale lattices
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