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Baire number of the spaces of uniform ultrafilters

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Abstract

The Baire number is defined for a topological space without isolated points as the minimal size of the family of nowhere dense sets covering the space in question. We prove that in the case ofU(κ), the space of uniform ultrafilters over uncountable κ, the Baire number equals eitherω 1 orω 2, depending on the cofinality of κ. The results are connected to the collapsing of cardinals when using the quotient algebraP(κ) mod[κ]<κ as the notion of forcing.

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Authors and Affiliations

  1. Matematický Ústav AV ČR, Žitná 25, 11567, Praha 1, Czech Republic

    Bohuslav Balcar

  2. Matematický Ústav University Karlovy, Sokolovská 83, 18600, Praha 8, Czech Republic

    Petr Simon

Authors
  1. Bohuslav Balcar
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  2. Petr Simon
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Additional information

The main portion of the present research, was done at the Center for Theoretical Study at Charles University and the Academy of Sciences.

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Balcar, B., Simon, P. Baire number of the spaces of uniform ultrafilters. Israel J. Math. 92, 263–272 (1995). https://doi.org/10.1007/BF02762081

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  • DOI: https://doi.org/10.1007/BF02762081

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