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 language | English |
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Pages (from-to) | 2719-2724 |
Number of pages | 6 |
Journal | Proceedings of the American Mathematical Society |
Volume | 125 |
Issue number | 9 |
DOIs | |
State | Published - 1997 |
Keywords
- Ramsey's theorem
- Rothberger property
- Square bracket partition relation