Pointfree forms of Dowker's and Michael's insertion theorems

DOI10.1016/j.jpaa.2008.05.010zbMath1154.06006OpenAlexW2079808228MaRDI QIDQ952248

Jorge Picado, Javier Gutiérrez García, Tomasz Kubiak

Publication date: 11 November 2008

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.2008.05.010

zbMATH Keywords

framenormalsemicontinuousperfectly normalinsertion theorempointfree topologycountably paracompact

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) Real-valued functions in general topology (54C30)

Related Items (21)

Normal semicontinuity and the Dedekind completion of pointfree function rings ⋮ Pseudocompleteness in the category of locales ⋮ Perfect locales and localic real functions ⋮ On the parallel between normality and extremal disconnectedness ⋮ Measurable functions on \(\sigma\)-frames ⋮ Separating families of locale maps and localic embeddings ⋮ Unnamed Item ⋮ Rings of real functions in pointfree topology ⋮ A preservation result for completely regular locales. ⋮ A lattice-theoretic approach to arbitrary real functions on frames ⋮ General insertion and extension theorems for localic real functions ⋮ Isocompactness in the category of locales. ⋮ Insertion of continuous real functions on spaces, bispaces, ordered spaces and pointfree spaces -- a common root ⋮ More on locales in which every open sublocale is \(z\)-embedded ⋮ Insertion theorems for countably paracompact frames and stratifiable frames ⋮ Localic real functions: A general setting ⋮ Covering maximal ideals with minimal primes ⋮ Tightness relative to some (co)reflections in topology ⋮ Completely normal frames and real-valued functions ⋮ Perfectness in locales ⋮ A Boolean extension of a frame and a representation of discontinuity

Cites Work

• Continuous selections. I
• Insertion of lattice-valued and hedgehog-valued functions
• On the algebraic representation of semicontinuity
• A new look at some classical theorems on continuous functions on normal spaces
• Monotone insertion and monotone extension of frame homomorphisms
• A new look at localic interpolation theorems
• Some characterizations of normal and perfectly normal spaces
• Compactification of Frames
• Realcompact spaces and regular σ -frames
• Dimension Theory for Σ-Frames
• A Sufficient Condition for the Insertion of a Continuous Function
• On Countably Paracompact Spaces
• On Real-Valued Functions in Topological Spaces
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