- Tytuł:
- On infinite partitions of lines and space
- Autorzy:
-
Erdös, Paul
Jackson, Steve
Mauldin, R. - Powiązania:
- https://bibliotekanauki.pl/articles/1205459.pdf
- Data publikacji:
- 1997
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
transfinite recursion
Martin's Axiom
forcing
geometry
infinite partitions - Opis:
- 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.
- Źródło:
-
Fundamenta Mathematicae; 1997, 152, 1; 75-95
0016-2736 - Pojawia się w:
- Fundamenta Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł