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A constructive Galois connection between closure and interior
Journal of Symbolic Logic 77 (4):1308-1324 (2012)
Abstract
We construct a Galois connection between closure and interior operators on a given set. All arguments are intuitionistically valid. Our construction is an intuitionistic version of the classical correspondence between closure and interior operators via complementLinks
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Citations of this work
Positivity relations on a locale.Francesco Ciraulo & Steven Vickers - 2016 - Annals of Pure and Applied Logic 167 (9):806-819.
Embedding locales and formal topologies into positive topologies.Francesco Ciraulo & Giovanni Sambin - 2018 - Archive for Mathematical Logic 57 (7-8):755-768.
Factorizing the $$\mathbf {Top}$$ Top – $$\mathbf {Loc}$$ Loc adjunction through positive topologies.Francesco Ciraulo, Tatsuji Kawai & Samuele Maschio - 2021 - Archive for Mathematical Logic 60 (7):967-979.
Factorizing the Top\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {Top}$$\end{document}–Loc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {Loc}$$\end{document} adjunction through positive topologies. [REVIEW]Francesco Ciraulo, Tatsuji Kawai & Samuele Maschio - 2021 - Archive for Mathematical Logic 60 (7-8):967-979.
References found in this work
Inductively generated formal topologies.Thierry Coquand, Giovanni Sambin, Jan Smith & Silvio Valentini - 2003 - Annals of Pure and Applied Logic 124 (1-3):71-106.
Positivity relations on a locale.Francesco Ciraulo & Steven Vickers - 2016 - Annals of Pure and Applied Logic 167 (9):806-819.
Formal topologies on the set of first-order formulae.Thierry Coquand, Sara Sadocco, Giovanni Sambin & Jan M. Smith - 2000 - Journal of Symbolic Logic 65 (3):1183-1192.
Regular opens in constructive topology and a representation theorem for overlap algebras.Francesco Ciraulo - 2013 - Annals of Pure and Applied Logic 164 (4):421-436.
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