π(X) = δ(X) for compact X

I. Juhász*, S. Shelah

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

We prove that if X is a compact T2 space (and x ε{lunate} X) and π(X)=κ (πχ(x, X)=κ), then there is a dense subset Y ⊂ X (resp. a set Y ⊂ X with x ε{lunate} Ȳ) such that d(Y)=κ (resp. x∉Z̄ for any Z ⊂ Y with |Z|<κ). Previously this only has been proven for κ regular. A consequence is that the point-picking game GD α(X) is always determined if X is compact T2.

Original languageEnglish
Pages (from-to)289-294
Number of pages6
JournalTopology and its Applications
Volume32
Issue number3
DOIs
StatePublished - Aug 1989

Keywords

  • Boolean algebra of regular open subsets
  • compact
  • dense set
  • point-picking game
  • singular cardinals
  • π-weight

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