Discrete n-tuples in Hausdorff spaces

Timothy J. Carlson, Neil Hindman, and Dona Strauss. "Discrete n-tuples in Hausdorff spaces." Fundamenta Mathematicae 187.2 (2005): 111-126. <http://eudml.org/doc/282972>.

@article{TimothyJ2005,
abstract = {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.},
author = {Timothy J. Carlson, Neil Hindman, Dona Strauss},
journal = {Fundamenta Mathematicae},
keywords = {Ramsey theory; -Ramsey filter; -Ramsey limit; -tuples},
language = {eng},
number = {2},
pages = {111-126},
title = {Discrete n-tuples in Hausdorff spaces},
url = {http://eudml.org/doc/282972},
volume = {187},
year = {2005},
}

TY - JOUR
AU - Timothy J. Carlson
AU - Neil Hindman
AU - Dona Strauss
TI - Discrete n-tuples in Hausdorff spaces
JO - Fundamenta Mathematicae
PY - 2005
VL - 187
IS - 2
SP - 111
EP - 126
AB - 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.
LA - eng
KW - Ramsey theory; -Ramsey filter; -Ramsey limit; -tuples
UR - http://eudml.org/doc/282972
ER -