On a topological Ramsey Theorem
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 $r>1$
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2021
- DOI:
- 10.48550/arXiv.2111.14729
- arXiv:
- arXiv:2111.14729
- Bibcode:
- 2021arXiv211114729K
- Keywords:
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- Mathematics - General Topology;
- 03E02;
- 54A20;
- 54D30
- E-Print:
- 10 pages