Wszystkie pola: Jackson, Paul - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: On partitions of lines and space
Autorzy:: Erdös, Paul
Jackson, Steve
Mauldin, R.
Powiązania:: https://bibliotekanauki.pl/articles/1208480.pdf
Data publikacji:: 1994
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: transfinite recursion
Opis:: 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 $ω_θ$.
Źródło:: Fundamenta Mathematicae; 1994, 145, 2; 101-119
0016-2736
Pojawia się w:: Fundamenta Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: On infinite partitions of lines and space
Autorzy:: Erdös, Paul
Jackson, Steve
Mauldin, R.
Powiązania:: https://bibliotekanauki.pl/articles/1205459.pdf
Data publikacji:: 1997
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: transfinite recursion
Martin's Axiom
forcing
geometry
infinite partitions
Opis:: Given a partition P:L → ω of the lines in $ℝ^n$, n ≥ 2, into countably many pieces, we ask if it is possible to find a partition of the points, $Q:ℝ^n → ω$, so that each line meets at most m points of its color. Assuming Martin's Axiom, we show this is the case for m ≥ 3. We reduce the problem for m = 2 to a purely finitary geometry problem. Although we have established a very similar, but somewhat simpler, version of the geometry conjecture, we leave the general problem open. We consider also various generalizations of these results, including to higher dimension spaces and planes.
Źródło:: Fundamenta Mathematicae; 1997, 152, 1; 75-95
0016-2736
Pojawia się w:: Fundamenta Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

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