Corollary 1
Tag 0BLL, permanent. Cite it as [Bourbaki, Tag 0BLL].
General Topology, chapter III, § 4. Groups operating properly on a topological space; compact ness in topological groups and spaces with operators
If is a totally disconnected locally compact group, then every neighbourhood of in contains an open subgroup of .
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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Nothing.