Does someone know any example of a locally compact but not locally connected group?
Thank you
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1Any locally profinite group, e.g. the additive group of a local field, the multiplicative group of a local field, $\operatorname{GL}_n$ of a local field (non-archimedean local fields) – Edward Evans Oct 13 '20 at 14:25
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The Cantor set is locally compact but not locally connected. – Chrystomath Oct 13 '20 at 14:32
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There are even connected locally compact groups that are not locally connected. – YCor Oct 18 '20 at 21:23
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@EdwardEvans Not every locally profinite groups, every non-discrete locally profinite group ;-) – Cronus Oct 20 '20 at 10:54
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Thank you guys! – Nov 24 '20 at 10:01