On partitions of lines and space

Volume 145 / 1994

P. Erdős, Steve Jackson, R. Daniel Mauldin Fundamenta Mathematicae 145 (1994), 101-119 DOI: 10.4064/fm-145-2-101-119


We consider a set, L, of lines in $ℝ^n$ and a partition of L into some number of sets: $L = L_1∪...∪ L_p$. We seek a corresponding partition $ℝ^n = S_1 ∪...∪ S_p$ such that each line l in $L_i$ meets the set $S_i$ in a set whose cardinality has some fixed bound, $ω_τ$. We determine equivalences between the bounds on the size of the continuum, $2^ω ≤ ω_θ$, and some relationships between p, $ω_τ$ and $ω_θ$.


  • P. Erdős
  • Steve Jackson
  • R. Daniel Mauldin

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