Remark 2

Tag 0BN7, permanent. Cite it as [Bourbaki, Tag 0BN7].

General Topology, chapter III, § 6. Topological groups with operators; topological rings division rings and fields

If a Hausdorff commutative topological group with operators is the topological direct sum of a family $(M_i)_{1 \leq i \leq n}$ of stable subgroups, then each of the subgroups $M_i$ is closed in $E$ , for $M_i$ is the set of all $x \in E$ such that $p_i(x) = x$ (Chapter I, § 8, no. 1, Proposition 2).

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

Nothing.

Cites

Chapter I, § 8, no. 1, Proposition 2