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## Fundamenta Mathematicae

1997 | 152 | 1 | 75-95
Tytuł artykułu

### On infinite partitions of lines and space

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Given a partition P:L → ω of the lines in $ℝ^n$, n ≥ 2, into countably many pieces, we ask if it is possible to find a partition of the points, $Q:ℝ^n → ω$, so that each line meets at most m points of its color. Assuming Martin's Axiom, we show this is the case for m ≥ 3. We reduce the problem for m = 2 to a purely finitary geometry problem. Although we have established a very similar, but somewhat simpler, version of the geometry conjecture, we leave the general problem open. We consider also various generalizations of these results, including to higher dimension spaces and planes.
Słowa kluczowe
EN
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
75-95
Opis fizyczny
Daty
wydano
1997
otrzymano
1996-06-27
Twórcy
autor
• Mathematical Institute, Hungarian Academy of Sciences, Reáltanoda U. 13-15, H-1053 Budapest, Hungary
autor
• Department of Mathematics, University of North Texas, Denton, Texas 76203-5116, U.S.A.
autor
• Department of Mathematics, University of North Texas, Denton, Texas 76203-5116, U.S.A.
Bibliografia
• [1] R. Davies, On a denumerable partition problem of Erdős, Proc. Cambridge Philos. Soc. 59 (1963), 33-36.
• [2] P. Erdős, S. Jackson and R. D. Mauldin, On partitions of lines and space, Fund. Math. 145 (1994), 101-119.
• [3] S. Jackson and R. D. Mauldin, Set Theory and Geometry, to appear.
• [4] T. Jech, Set Theory, Academic Press, 1978.
• [5] K. Kunen, Set Theory, an Introduction to Independence Proofs, North-Holland, 1980.
• [6] S. Todorčević, Partitioning pairs of countable ordinals, Acta Math. 159 (1987), 261-294.
Typ dokumentu
Bibliografia
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