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Proceedings of the American Mathematical SocietyVolume 150, Issue 7, 1 July 2022, Pages 3177-3187

DENSE METRIZABLE SUBSPACES IN POWERS OF CORSON COMPACTA(Article)(Open Access)

  • Leiderman, A.,
  • Spadaro, S.,
  • Todorcevic, S.
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  • aDepartment of Mathematics, Ben Gurion University of the Negev, P.O.B. 653, Be'er Sheva, 8410501, Israel
  • bDipartimento di Ingegneria, Università degli Studi di Palermo, viale delle Scienze 8, Palermo, 90128, Italy
  • cDepartment of Mathematics, University of Toronto, Toronto, ON M5S 2E4, Canada
  • dInstitut de Mathématiques de Jussieu, Paris, France
  • eMathematical Institute, SASA, Belgrade, Serbia

Abstract

We characterize when the countable power of a Corson compactum has a dense metrizable subspace and construct consistent examples of Corson compacta whose countable power does not have a dense metrizable subspace. We also give several remarks about ccc Corson compacta and, as a byproduct, we obtain a new proof of Kunen and van Mill's characterization of when a Corson compactum supporting a strictly positive measure is metrizable. © 2022 American Mathematical Society

Author keywords

Corson compactumcountable chain conditiondense metrizable subspaceMartin's Axiomstrictly positive measure

Funding details

Funding sponsor Funding number Acronym
Natural Sciences and Engineering Research Council of Canada
See opportunities by NSERC		455916NSERC
Centre National de la Recherche ScientifiqueUMR7586CNRS
Ben-Gurion University of the NegevBGU

  • 1

    Received by the editors July 5, 2021, and, in revised form, October 3, 2021. 2020 Mathematics Subject Classification. Primary 54A25, 54A35, 03E35, 46B50. Key words and phrases. Corson compactum, dense metrizable subspace, countable chain condition, Martin’s Axiom, strictly positive measure. The second author was partially financially supported by INdAM-GNSAGA and by the Center for Advanced Studies in Mathematics at Ben Gurion University during his visit to Be’er Sheva in 2018. The research of the third author was partially supported by grants from NSERC (455916) and CNRS (UMR7586).

  • ISSN: 00029939
  • Source Type: Journal
  • Original language: English
  • DOI: 10.1090/proc/15885
  • Document Type: Article
  • Publisher: American Mathematical Society


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