The Loomis-Sikorski Theorem revisited

• Autores: Gerard Buskes, Ben de Pagter , A. van Rooij
• Localización: Algebra universalis, ISSN 0002-5240, Vol. 58, Nº. 4, 2008, págs. 413-426
• Idioma: inglés
• DOI: 10.1007/s00012-008-2077-x
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• Resumen

  • We prove, constructively, that the Loomis�Sikorski Theorem for ?-complete Boolean algebras follows from a representation theorem for Archimedean vector lattices and a constructive representation of Boolean algebras as spaces of Carathéodory place functions. We also prove a constructive subdirect product representation theorem for arbitrary partially ordered vector spaces.