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*Question (research)

within loc compact T2 groups,

+ what makes Lie groups different to prof. groups is that they have a small neighbourhood from which every closed subgroup escapes

+ and (locally) prof. groups don't have such a neighbourhood for open subgroups

(1/x)
It's sad we have to require small subgroups but not for closed subgroups but for something even much stronger

open subgroups

but that also means that there is a structure in between? what is it like?
What are the locally compact Haussdorf groups G such that for every neighbourhood U of 1_G there is a closed nontrivial subgroup H \subseteq U...

...but still there is a neighbourhood U_0 of 1_G such that every open subgroup H of G escapes U_0?

#LieGroups #TopologicalGroups
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