Definition 1
Tag 0BZR, permanent. Cite it as [Bourbaki, Tag 0BZR].
General Topology, chapter VII, § 3. Infinite sums in the groups $\mathbf{R}^n$
A series of points of is said to be absolutely convergent if the series of Euclidean norms of its terms is convergent.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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