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Why every non-discrete locally compact group contains a nontrivial convergent sequence?

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    Please only use $\LaTeX$ to format mathematics.2012-12-23
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    in myresearch i got it2012-12-23
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    This seems like the sort of question whose answer might be found in the first couple of chapters of *Differential Geometry, Lie Groups, and Symmetric Spaces* by Helgason. (I don't have a copy with me or else I'd have checked.)2012-12-23
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    It seems that non-discreteness implies that any neighborhood of identity contains infinitely many distinct elements, and compactness allows you to choose a convergent sequence out of them...2012-12-23
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    @PavelM No, as compact does not imply sequentially compact in general.2012-12-23

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