Remark 2

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

General Topology, chapter IX, Appendix 2. Produits infinis dans les algèbres normées

Def. 1 generalizes immediately to the case of a family $(\mathbf{x}_n)_{n \in I}$ whose set of indices $I$ is a subset of $\mathbf{Z}$ (totally ordered by the order induced by that of $\mathbf{Z}$ ); we leave to the reader the task of extending to this case the following properties (cf. IX, p. 125, exerc. 1 and 2).

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

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