The Stone-Čech compactification of a partial frame via ideals and cozero elements

DOI10.2989/16073606.2015.1023866zbMath1436.06010OpenAlexW2290465282MaRDI QIDQ5233907

Anneliese Schauerte, J. L. Frith

Publication date: 9 September 2019

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

Full work available at URL: https://doi.org/10.2989/16073606.2015.1023866

zbMATH Keywords

idealframemeet-semilatticeStone-Čech compactificationcategory equivalencecompletely regular frameselection function\(\kappa\)-frame\(\sigma\)-framecoreflection\(\mathcal{S}\)-framepartial framecompact frame\(\mathcal{S}\)-cozero element\(\mathcal{S}\)-ideal\(\mathcal{S}\)-Lindelöf elementco-zero

Mathematics Subject Classification ID

Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) (18A40) Compactness (54D30) Noncompact covering properties (paracompact, Lindelöf, etc.) (54D20) Categorical methods in general topology (54B30) Frames, locales (06D22) Extensions of spaces (compactifications, supercompactifications, completions, etc.) (54D35) Lattice ideals, congruence relations (06B10) Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.) (54D15) Semilattices (06A12)

Related Items (10)

A look at the structure of congruence frames by means of Heyting congruences ⋮ Variants of Booleanness: congruences of a partial frame versus those of its free frame ⋮ Reflectors to quantales ⋮ Closed and open maps for partial frames ⋮ The congruence frame and the Madden quotient for partial frames ⋮ Completions of uniform partial frames ⋮ Coverages give free constructions for partial frames ⋮ Meet-semilattice congruences on a frame ⋮ Compactifications and reflections of partial spaces via partial frames ⋮ Partial frames and filter spaces

Cites Work

• A Shirota theorem for frames
• Categories of partial frames
• \(\kappa\)-frames
• Coz-onto frame maps and some applications
• Frames and Locales
• Alexandroff Algebras and Complete Regularity
• Lindelöf locales and realcompactness
• Stone-čech Compactification and Dimension Theory for Regular σ-Frames
• On projective Z-frames
• THE FRAME ENVELOPE OF A σ-FRAME
• Aspects of nearness in σ-frames
• Realcompactness and the cozero part of a frame
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