Given a topological group $G$ can we embbed it in $Aut_{TOP}(X)$ for some topological space $X$?
It is a good choice the open-compact topology for $Aut_{TOP}(X)$?
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Since the usual proof gives an embedding in the group sense, I assume you mean an embedding in the topological sense? – Tobias Kildetoft Oct 23 '17 at 05:40
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Yes, in the topological sense. – Math.mx Oct 23 '17 at 11:49
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1$X = G$ should work fine at least if $G$ is locally compact Hausdorff. General topological groups are a mess, and so are general topological spaces, so... – Qiaochu Yuan Oct 23 '17 at 18:10
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1Yes, there is – Bumblebee Feb 02 '23 at 06:44