Remark 1
Tag 0BN6, permanent. Cite it as [Bourbaki, Tag 0BN6].
General Topology, chapter III, § 6. Topological groups with operators; topological rings division rings and fields
To avoid confusion, we shall sometimes say that a stable subgroup of which is a complement of (in the sense of the structure of group with operators, without a topology) is an algebraic complement of .
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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