Remark 3
Tag 0BME, permanent. Cite it as [Bourbaki, Tag 0BME].
General Topology, chapter III, § 5. Infinite sums in commutative groups
Definition 1 applies, more generally, to every family of points in a Hausdorff topological space on which has been defined an associative and commutative law of composition, written additively; for it does not make use of the axioms of topological groups.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.