WEISS'S QUESTION
There is a function f:R+→{0,1} such that if F(x,y)=f(d(x,y)) (d(x,y) is the distance between x and y), then there is no uncountable homogeneous set for F. If CH holds, we show that there is a similar coloring of Rn with ℵ1 colors so that uncountable sets contain all colors.
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| Veröffentlicht in: | Mathematika 2020-10, Vol.66 (4), p.954-958 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
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| Online-Zugang: | Volltext |
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| Zusammenfassung: | There is a function f:R+→{0,1} such that if F(x,y)=f(d(x,y)) (d(x,y) is the distance between x and y), then there is no uncountable homogeneous set for F. If CH holds, we show that there is a similar coloring of Rn with ℵ1 colors so that uncountable sets contain all colors. |
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| ISSN: | 0025-5793 2041-7942 |
| DOI: | 10.1112/mtk.12053 |