Displaying similar documents to “On the planar translation structures”

On infinite partitions of lines and space

Paul Erdös, Steve Jackson, R. Mauldin (1997)

Fundamenta Mathematicae

Similarity:

Given a partition P:L → ω of the lines in n , n ≥ 2, into countably many pieces, we ask if it is possible to find a partition of the points, Q : 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...