A Boolean extension of a frame and a representation of discontinuity

DOI10.2989/16073606.2017.1348399zbMath1436.06026OpenAlexW2748446518MaRDI QIDQ5236135

Jorge Picado, Ales Pultr

Publication date: 15 October 2019

Published in: Quaestiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2989/16073606.2017.1348399

zbMATH Keywords

localeframeregularsublocaleclosed sublocaleopen sublocalereal functionsublocale latticelower and upper regularizationssubfitlower and upper semicontinuities

Mathematics Subject Classification ID

Frames, locales (06D22) Real-valued functions in general topology (54C30)

Related Items (10)

Exact and strongly exact filters ⋮ Maximal essential extensions in the context of frames ⋮ Observables on \(\sigma\)-frame effect algebras as upper semicontinuous functions ⋮ Perfect locales and localic real functions ⋮ On the categorical behaviour of locales and D-localic maps ⋮ On the universal completion of pointfree function spaces ⋮ Exact filters and joins of closed sublocales ⋮ A lattice-theoretic approach to arbitrary real functions on frames ⋮ On joins of complemented sublocales ⋮ Some aspects of (non) functoriality of natural discrete covers of locales

Cites Work

• On an aspect of scatteredness in the point-free setting
• 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
• More on subfitness and fitness
• A new look at localic interpolation theorems
• Frames and Locales
• The lattice theoretic part of topological separation properties
• Atomless Parts of Spaces.
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