Stone-čech Compactification and Dimension Theory for Regular σ-Frames

DOI10.1112/JLMS/S2-39.1.1zbMath0675.06005OpenAlexW2079214621MaRDI QIDQ3829590

Bernhard Banaschewski, Christopher Gilmour

Publication date: 1989

Published in: Journal of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1112/jlms/s2-39.1.1

zbMATH Keywords

Stone-Čech compactification of a regular \(\sigma\)-frame

Mathematics Subject Classification ID

Complete lattices, completions (06B23) Topological spaces and generalizations (closure spaces, etc.) (54A05) Topological lattices, etc. (topological aspects) (54H12) Topological lattices (06B30)

Related Items (33)

THE FRAME ENVELOPE OF A σ-FRAME ⋮ REAL IDEALS IN POINTFREE RINGS OF CONTINUOUS FUNCTIONS ⋮ \(\kappa\)-frames ⋮ Covering dimension and universality property on frames ⋮ Compactifications, \(A\)-compactifications and proximities ⋮ Generating sublocales by subsets and relations: a tangle of adjunctions ⋮ Which distributive lattices are lattices of open sets of \(P\)-spaces? ⋮ On a generalization of pointfree realcompactness ⋮ \((\mathcal Z_1,\mathcal Z_2)\)-complete partially ordered sets and their representations by \(\mathcal Q\)-spaces. ⋮ Compactifications and A-compactifications of frames. Proximal frames ⋮ The Katětov-Morita theorem for the dimension of metric frames ⋮ Unnamed Item ⋮ Nearly realcompact frames. ⋮ Characterizing realcompact locales via remainders ⋮ A study of a new dimension for frames ⋮ Connectedness extended to \(\sigma\)-frames ⋮ A NOTE ON RELATIVE PSEUDOCOMPACTNESS IN THE CATEGORY OF FRAMES ⋮ A method for constructing coreflections for nearness frames. ⋮ Universality property and dimension for frames ⋮ Coproducts in the category \(\mathbf M\kappa\mathbf{Frm}\) ⋮ Unnamed Item ⋮ Samuel compactification and uniform coreflection of nearness σ-frames ⋮ \(z\)-ideals in the real continuous function ring \(\mathcal{R}(L_{\tau}) \) ⋮ More on locales in which every open sublocale is \(z\)-embedded ⋮ The Stone-Čech compactification of a partial frame via ideals and cozero elements ⋮ Tightness relative to some (co)reflections in topology ⋮ A study of the quasi covering dimension of finite lattices ⋮ Complete nearness \(\sigma\)-frames ⋮ Uniformly locally connected uniform \(\sigma\)-frames ⋮ A study of a covering dimension of finite lattices ⋮ A study of covering dimension for the class of finite lattices. ⋮ THE WALLMAN COMPACTIFICATION OF FRAMES ⋮ Remarks on the frame envelope of a sigma-frame

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