Corollary 2

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

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

If $(x_n)$ is a multipliable sequence whose product is invertible in $A$ , any sequence $(x_{n_k})_{k \in \mathbf{N}}$ extracted from $(x_n)$ (( $n_k$ ) being a strictly increasing sequence of integers) is multipliable.

This is what the criterion of th. 1 ( $IX$ , p. 79) immediately shows.

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

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