Open covers and the square bracket partition relation

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Abstract

An open cover u of an infinite separable metric space X is an w-cover of X if X ∌ u and for every finite subset F of X there is a U ε u such that F ⊆ U. Let fi be the collection of ω-covers of X. We show that the partition relation Ω → [Ω]2/2 holds if, and only if, the partition relation Ω → [Ω]2/3 holds.

Original languageEnglish
Pages (from-to)2719-2724
Number of pages6
JournalProceedings of the American Mathematical Society
Volume125
Issue number9
DOIs
StatePublished - 1997

Keywords

  • Ramsey's theorem
  • Rothberger property
  • Square bracket partition relation

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