Countable partitions of the sets of points and lines
James Schmerl (1999)
Fundamenta Mathematicae
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The following theorem is proved, answering a question raised by Davies in 1963. If is a partition of the set of lines of , then there is a partition such that whenever . There are generalizations to some other, higher-dimensional subspaces, improving recent results of Erdős, Jackson Mauldin.