Israel Journal of Mathematics

, Volume 92, Issue 1–3, pp 263–272 | Cite as

Baire number of the spaces of uniform ultrafilters

  • Bohuslav Balcar
  • Petr Simon
Article
Received:
Revised:

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.

Keywords

Topological Space Regular Cardinal Force Notion Disjoint Family Infinite Cardinal 
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Copyright information

© Hebrew University 1995

Authors and Affiliations

  • Bohuslav Balcar
    • 1
  • Petr Simon
    • 2
  1. 1.Matematický Ústav AV ČRPraha 1Czech Republic
  2. 2.Matematický Ústav University KarlovyPraha 8Czech Republic

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