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

Question

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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 $g_i\in U.$