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 
@article{10_4064_fm_145_2_101_119,
     author = {P. Erd\H{o}s and Steve  Jackson and R. Daniel Mauldin},
     title = {On partitions of lines and space},
     journal = {Fundamenta Mathematicae},
     pages = {101--119},
     publisher = {mathdoc},
     volume = {145},
     number = {2},
     year = {1994},
     doi = {10.4064/fm-145-2-101-119},
     language = {fr},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/fm-145-2-101-119/}
}
TY  - JOUR
AU  - P. Erdős
AU  - Steve  Jackson
AU  - R. Daniel Mauldin
TI  - On partitions of lines and space
JO  - Fundamenta Mathematicae
PY  - 1994
SP  - 101
EP  - 119
VL  - 145
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/fm-145-2-101-119/
DO  - 10.4064/fm-145-2-101-119
LA  - fr
ID  - 10_4064_fm_145_2_101_119
ER  - 
%0 Journal Article
%A P. Erdős
%A Steve  Jackson
%A R. Daniel Mauldin
%T On partitions of lines and space
%J Fundamenta Mathematicae
%D 1994
%P 101-119
%V 145
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/fm-145-2-101-119/
%R 10.4064/fm-145-2-101-119
%G fr
%F 10_4064_fm_145_2_101_119
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. http://geodesic.mathdoc.fr/articles/10.4064/fm-145-2-101-119/

Cité par Sources :