Discrete n-tuples in Hausdorff spaces

• Autorzy: Timothy J. Carlson , Neil Hindman , Dona Strauss
• Języki publikacji: EN

Abstrakty

EN

We investigate the following three questions: Let n ∈ ℕ. For which Hausdorff spaces X is it true that whenever Γ is an arbitrary (respectively finite-to-one, respectively injective) function from ℕⁿ to X, there must exist an infinite subset M of ℕ such that Γ[Mⁿ] is discrete? Of course, if n = 1 the answer to all three questions is "all of them". For n ≥ 2 the answers to the second and third questions are the same; in the case n = 2 that answer is "those for which there are only finitely many points which are the limit of injective sequences". The answers to the remaining instances involve the notion of n-Ramsey limit. We also show that the class of spaces satisfying these discreteness conclusions for all n includes the class of F-spaces. In particular, it includes the Stone-Čech compactification of any discrete space.

Kategorie tematyczne

• 05D10: Ramsey theory
• 54A20: Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2005
• Tom: 187
• Numer: 2
• Strony: 111-126

Daty

wydano

2005

Twórcy

autor

Timothy J. Carlson

• Department of Mathematics, Ohio State University, Columbus, OH 43210, U.S.A.

autor

Neil Hindman

• Department of Mathematics, Howard University, Washington, DC 20059, U.S.A.

autor

Dona Strauss

• Department of Pure Mathematics, University of Hull, Hull HU6 7RX, UK

Identyfikatory

DOI

10.4064/fm187-2-2