On partitions of lines and space

Erdös, Paul; Jackson, Steve; Mauldin, R.

Erdös, Paul ; Jackson, Steve ; Mauldin, R.

Fundamenta Mathematicae, Tome 144 (1994), p. 101-119 / Harvested from The Polish Digital Mathematics Library

Résumé

We consider a set, L, of lines in $ℝ^{n}$ and a partition of L into some number of sets: $L = L_{1} \cup . . . \cup L_{p}$ . We seek a corresponding partition $ℝ^{n} = S_{1} \cup . . . \cup S_{p}$ 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, $2^{ω} \leq ω_{θ}$ , and some relationships between p, $ω_{τ}$ and $ω_{θ}$ .

Publié le : 1994-01-01

Zbl 0809.04004

EUDML-ID : urn:eudml:doc:212037

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     author = {Paul Erd\"os and Steve Jackson and R. Mauldin},
     title = {On partitions of lines and space},
     journal = {Fundamenta Mathematicae},
     volume = {144},
     year = {1994},
     pages = {101-119},
     zbl = {0809.04004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv145i2p101bwm}
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Erdös, Paul; Jackson, Steve; Mauldin, R. On partitions of lines and space. Fundamenta Mathematicae, Tome 144 (1994) pp. 101-119. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv145i2p101bwm/

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