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Curve Selection Lemma for semianalytic sets and conjugacy classes of finite order in Lie groups

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 نشر من قبل Jinpeng An
 تاريخ النشر 2005
  مجال البحث
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Using a strong version of the Curve Selection Lemma for real semianalytic sets, we prove that for an arbitrary connected Lie group $G$, each connected component of the set $E_n(G)$ of all elements of order $n$ in $G$ is a conjugacy class in $G$. In particular, all conjugacy classes of finite order in $G$ are closed. Some properties of connected components of $E_n(G)$ are also given.



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