Geodesic
On a topological Ramsey theorem
Canadian mathematical bulletin, Tome 66 (2023) no. 1, pp. 156-165

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DOI

We introduce natural strengthenings of sequential compactness, 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 Continuum Hypothesis (CH) for all $r>1$). Productivity of the r-Ramsey property is considered.
DOI : 10.4153/S0008439522000170
Mots-clés : Sequentially compact, Ramsey’s theorem, almost disjoint families 
Kubiś, Wiesław; Szeptycki, Paul. On a topological Ramsey theorem. Canadian mathematical bulletin, Tome 66 (2023) no. 1, pp. 156-165. doi: 10.4153/S0008439522000170
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     title = {On a topological {Ramsey} theorem},
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     pages = {156--165},
     year = {2023},
     volume = {66},
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     doi = {10.4153/S0008439522000170},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439522000170/}
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