Remark 2

Tag 0C0Q, permanent. Cite it as [Bourbaki, Tag 0C0Q].

General Topology, chapter VIII, § 3. Infinite sums and products of complex numbers

As already remarked for products of factors $> 0$ , the convergence of the series with general term $u_n$ is neither necessary nor sufficient for the convergence of the product with general factor $1 + u_n$ .

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

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