Formal topology and constructive mathematics: the Gelfand and Stone-Yosida representation theorems

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dc.creatorCoquand, Thierry
dc.creatorSpitters, Bas
dc.date2008-08-20
dc.date.accessioned2026-07-07T09:57:29Z
dc.date.available2026-07-07T09:57:29Z
dc.descriptionWe present a constructive proof of the Stone-Yosida representation theorem for Riesz spaces motivated by considerations from formal topology. This theorem is used to derive a representation theorem for f-algebras. In turn, this theorem implies the Gelfand representation theorem for C*-algebras of operators on Hilbert spaces as formulated by Bishop and Bridges. Our proof is shorter, clearer, and we avoid the use of approximate eigenvalues.
dc.descriptionThis is an expanded version of our paper [CS05a]. For the convenience of the reader we have included more details and added a few clarifications. There are no new results. We are grateful to Bob Lubarsky and Fred Richman for suggesting improvements in the presentation
dc.identifierhttps://arxiv.org/abs/0808.2705
dc.identifierhttp://arxiv.org/abs/0808.2705
dc.identifierJournal of Universal computation, volume 11, issue 12 2005
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/167362
dc.subjectFunctional Analysis
dc.subjectLogic
dc.subject03F60; 46S30; 06D22
dc.titleFormal topology and constructive mathematics: the Gelfand and Stone-Yosida representation theorems
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