Timeline for The identity element of a compact group is a limit point of any "polynomial sequence"
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| Oct 23, 2012 at 16:31 | comment | added | user25235 | Thanks. There's an argument (also due to Bergelson I think !) which shows that Van der Waerden's theorem implies the theorem in my question : if $U$ is a small neighbourhood of the identity, $G$ has a finite covering by some $(g_iU)_i$, and any map $n\in \mathbb{N} \mapsto$ some $i$ with $g^{P(n)} \in g_iU$ defines a colouring of the integers to which Van der Waerden's theorem can be applied. On then concludes using equations like $(x+2y)^2-2(x+y)^2+x^2=2y^2$ and its generalizations. But since I've never considered Van der Waerden's theorem as "elementary" ... | |
| Oct 23, 2012 at 14:31 | history | answered | Ramiro de la Vega | CC BY-SA 3.0 |