Why every non-discrete locally compact group contains a nontrivial convergent sequence?
Non-discrete locally compact group
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$\begingroup$
general-topology
locally-compact-groups
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1Please only use $\LaTeX$ to format mathematics. – 2012-12-23
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0in myresearch i got it – 2012-12-23
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0This 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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0It 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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0@PavelM No, as compact does not imply sequentially compact in general. – 2012-12-23