Temat: infinite partitions - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Countable partitions of the sets of points and lines
Autorzy:: Schmerl, James
Powiązania:: https://bibliotekanauki.pl/articles/1205246.pdf
Data publikacji:: 1999
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: infinite partitions
Euclidean space
Opis:: The following theorem is proved, answering a question raised by Davies in 1963. If $L_0 ∪ L_1 ∪ L_2 ∪...$ is a partition of the set of lines of $ℝ^n$, then there is a partition $ℝ^n = S_0 ∪ S_1 ∪ S_2 ∪...$ such that $|ℓ ∩ S_i| ≤ 2$ whenever $ℓ ∈ L_i$. There are generalizations to some other, higher-dimensional subspaces, improving recent results of Erdős, Jackson & Mauldin.
Źródło:: Fundamenta Mathematicae; 1999, 160, 2; 183-196
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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