On a topological Ramsey theorem

0569942 - MÚ 2024 RIV CA eng J - Journal Article
Kubiś, Wieslaw - Szeptycki, P.
On a topological Ramsey theorem.
Canadian Mathematical Bulletin-Bulletin Canadien de Mathematiques. Roč. 66, č. 1 (2023), s. 156-165. ISSN 0008-4395. E-ISSN 1496-4287
R&D Projects: GA ČR(CZ) GX20-31529X
Institutional support: RVO:67985840
Keywords : almost disjoint families * Ramsey's theorem * sequentially compact
OECD category: Pure mathematics
Impact factor: 0.6, year: 2022
Method of publishing: Open access
https://doi.org/10.4153/S0008439522000170

We introduce natural strengthenings of sequential compactness, the r-Ramsey property for each natural number r≥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≥1 (assuming Continuum Hypothesis (CH) for all r > 1). Productivity of the r-Ramsey property is considered.
Permanent Link: https://hdl.handle.net/11104/0341259