On a topological Ramsey theorem

Speaker(s)

Paul Szeptycki

Affiliation

York University

Date

Dec. 8, 2021, 4:15 p.m.

Information about the event

Zoom

Seminar

Topology and Set Theory Seminar

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This is joint work with Wiesław Kubiś. 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 $r\geq 1$ (ZFC for $r=1$ and assuming CH for all $r>1$). The question of preservation in products will also be discussed.

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• slides