Geodesic
On partitions of lines and space
Fundamenta Mathematicae, Tome 145 (1994) no. 2, pp. 101-119

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 $ω_θ$.
DOI : 10.4064/fm-145-2-101-119
Mots-clés : transfinite recursion

P. Erdős 1 ; Steve Jackson 1 ; R. Daniel Mauldin 1

1 
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P. Erdős; Steve  Jackson; R. Daniel Mauldin. On partitions of lines and space. Fundamenta Mathematicae, Tome 145 (1994) no. 2, pp. 101-119. doi: 10.4064/fm-145-2-101-119

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