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Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: MatematicasVolume 116, Issue 4, October 2022, Article number 178

Ultrafilter selection and Corson compacta(Article)

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  • aLaboratoire de Mathématiques, Université de Savoie et Mont Blanc, Le Bourget-du-Lac, France
  • bCardinal Stefan Wyszynski University in Warsaw, Warsaw, Poland
  • cMatematicki Institut, SANU, Belgrade, Serbia
  • dDepartment of Mathematics, University of Toronto, Toronto, Canada

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Correction to: Ultrafilter selection and corson compacta (Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, (2022), 116, 4, (178), 10.1007/s13398-022-01317-2)

(2023) Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas, 117 (1), Article number 2

Abstract

We study the question which Boolean algebras have the property that for every generating set there is an ultrafilter selecting maximal number of its elements. We call it the ultrafilter selection property. For cardinality ℵ1 the property is equivalent to the fact that the space of ultrafilters is not Corson compact. We also consider the pointwise topology on a Boolean algebra, proving a result on the Lindelöf number in the context of the ultrafilter selection property. Finally, we discuss poset Boolean algebras, interval algebras, and semilattices in the context of ultrafilter selection properties. © 2022, The Author(s) under exclusive licence to The Royal Academy of Sciences, Madrid.

Author keywords

Boolean algebrasCorson compact spacsElementary submodelUltrafilter selectionValdivia compact spaces

Indexed keywords

Engineering controlled terms:Topology
Engineering uncontrolled termsCardinalitiesCorsa compact spacsElementary submodelGenerating setPoint wisePropertySubmodelsUltrafilter selectionUltrafiltersValdivium compact space
Engineering main heading:Boolean algebra

Funding details

Funding sponsor Funding number Acronym
7750027
Natural Sciences and Engineering Research Council of Canada
See opportunities by NSERC		NSERC
Grantová Agentura České Republiky20-22230LGA ČR
Centre National de la Recherche ScientifiqueUMR7586CNRS

  • 1

    R. Bonnet was supported by the Institute of Mathematics of the Czech Academy of Sciences, Prague.

  • 2

    The third author was partially supported by grants from NSERC (455916), CNRS (UMR7586) and SFRS(7750027).

  • 3

    W. Kubiś was supported by the GA ČR Grant 20-22230L (Czech Science Foundation)

  • ISSN: 15787303
  • Source Type: Journal
  • Original language: English
  • DOI: 10.1007/s13398-022-01317-2
  • Document Type: Article
  • Publisher: Springer-Verlag Italia s.r.l.

  Kubiś, W.; Cardinal Stefan Wyszynski University in Warsaw, Warsaw, Poland;
© Copyright 2022 Elsevier B.V., All rights reserved.

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