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arXiv · 2111.14729

On a topological Ramsey Theorem

Wiesław Kubiś·Paul Szeptycki
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Abstract

We introduce natural strengthenings of sequential compactness called the $r$-Ramsey property for each natural number $r\geq 1$. We prove that metrizable compact spaces are $r$-Ramsey for all $r$ and give examples of compact spaces that are $r$-Ramsey but not $r+1$-Ramsey for each $r\geq 1$ (assuming CH for all $r>1$

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Wiesław Kubiś, Paul Szeptycki. 2021-11-29. On a topological Ramsey Theorem. https://doi.org/10.4153/s0008439522000170

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