Exact approximations to Stone–Čech compactification

Annals of Pure and Applied Logic 146 (2):103-123 (2007)

Abstract
Given a locale L and any set-indexed family of continuous mappings , fi:L→Li with compact and completely regular co-domain, a compactification η:L→Lγ of L is constructed enjoying the following extension property: for every a unique continuous mapping exists such that . Considered in ordinary set theory, this compactification also enjoys certain convenient weight limitations.Stone–Čech compactification is obtained as a particular case of this construction in those settings in which the class of [0,1]-valued continuous mappings is a set for all L. This will follow by the proof that–also in the point-free context–a compactification that allows for the extension of [0,1]-valued mappings suffices for deriving the full reflection.A constructive proof that the class is a set whenever L is locally compact and L′ is set-presented and regular is also obtained; together with the described compactification, this makes it possible to characterize the class of locales for which Stone–Čech compactification can be defined constructively
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DOI 10.1016/j.apal.2006.12.004
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References found in this work BETA

Inductively Generated Formal Topologies.Thierry Coquand, Giovanni Sambin, Jan Smith & Silvio Valentini - 2003 - Annals of Pure and Applied Logic 124 (1-3):71-106.
Aspects of General Topology in Constructive Set Theory.Peter Aczel - 2006 - Annals of Pure and Applied Logic 137 (1):3-29.
On the Collection of Points of a Formal Space.Giovanni Curi - 2006 - Annals of Pure and Applied Logic 137 (1):126-146.
Maximal and Partial Points in Formal Spaces.Erik Palmgren - 2006 - Annals of Pure and Applied Logic 137 (1):291-298.

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Locatedness and Overt Sublocales.Bas Spitters - 2010 - Annals of Pure and Applied Logic 162 (1):36-54.

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