A short proof of Ellentuck's theorem (Q2701600)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A short proof of Ellentuck's theorem |
scientific article |
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19 February 2001
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Ellentuck topology
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completely Ramsey set
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Baire property
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A short proof of Ellentuck's theorem (English)
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The author offers a short proof of Ellentuck's theorem that characterizes the completely Ramsey subsets of \([\omega]^\omega\) as those having the Baire property with respect to what is now known as the Ellentuck topology. The key step is a technical lemma that readily implies the following two facts: Ellentuck open sets are completely Ramsey and the family of Ellentuck nowhere dense sets is closed under countable unions. From this the main theorem follows at once.
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