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Discrete n-tuples in Hausdorff spaces

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Carlson T., Hindman N., Strauss D.

Fundamenta Mathematicae

2005

tom 187

nr 2

111-126

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.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Carlson T.

1 Hindman N.

1 Strauss D.

1 2005

Wyniki wyszukiwania

Discrete n-tuples in Hausdorff spaces