# On partitions of lines and space

Paul Erdös; Steve Jackson; R. Mauldin

Fundamenta Mathematicae (1994)

- Volume: 145, Issue: 2, page 101-119
- ISSN: 0016-2736

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topErdös, Paul, Jackson, Steve, and Mauldin, R.. "On partitions of lines and space." Fundamenta Mathematicae 145.2 (1994): 101-119. <http://eudml.org/doc/212037>.

@article{Erdös1994,

abstract = {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 $ω_θ$.},

author = {Erdös, Paul, Jackson, Steve, Mauldin, R.},

journal = {Fundamenta Mathematicae},

keywords = {transfinite recursion; value of continuum; partitions of lines in Euclidean space; axiom of determinateness},

language = {eng},

number = {2},

pages = {101-119},

title = {On partitions of lines and space},

url = {http://eudml.org/doc/212037},

volume = {145},

year = {1994},

}

TY - JOUR

AU - Erdös, Paul

AU - Jackson, Steve

AU - Mauldin, R.

TI - On partitions of lines and space

JO - Fundamenta Mathematicae

PY - 1994

VL - 145

IS - 2

SP - 101

EP - 119

AB - 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 $ω_θ$.

LA - eng

KW - transfinite recursion; value of continuum; partitions of lines in Euclidean space; axiom of determinateness

UR - http://eudml.org/doc/212037

ER -

## References

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