Corollary 1

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

General Topology, chapter IX, Appendix 0. Infinite products in normed algebras

If the infinite product with general factor $x_n$ is convergent, and if $\prod_{n=0}^\infty x_n$ is a unit, then $\lim_{n \to \infty} x_n = e$ .

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

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