Proposition 4
Tag 0BZS, permanent. Cite it as [Bourbaki, Tag 0BZS].
General Topology, chapter VII, § 3. Infinite sums in the groups $\mathbf{R}^n$
A series of points of is commutatively convergent if and only if it is absolutely convergent.
This is a consequence of Proposition 9 of Chapter III, § 5, no. 7 and Theorem 1 above.
The examples given in Chapter IV, § 7 show that a series in can be convergent without being absolutely convergent.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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Nothing.