any element of open neighborhood of $e$ a connected lie group can be written as

Asked Aug 05 '12 at 21:54

Active Aug 05 '12 at 21:54

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About connected Lie Groups

Could any one give me hint for the problem?

Let $G$ be a connected Lie group, and $U$ an open neighborhood of the group unit $e$. Show that any $g\in G$ can be written as a product $g = g_1.\dots.g_N$ of elements $g_i\in U.$

edited Apr 13 '17 at 12:19

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asked Aug 05 '12 at 21:54

Myshkin

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Here's a hint: Let $X$ be the set of all $g\in G$ which can be written as such a product. Show that $X$ is both open and closed. – Jason DeVito - on hiatus Aug 05 '12 at 22:05
@JasonDeVito Thank you :) – Myshkin Aug 05 '12 at 22:32
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If you were able to figure it out from there, why not post your solution? – Jason DeVito - on hiatus Aug 05 '12 at 22:36

any element of open neighborhood of $e$ a connected lie group can be written as

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