Proposition 3

Tag 07AY, permanent. Cite it as [Bourbaki, Tag 07AY].

Topological Vector Spaces, chapter II, § 1. Semi-norms

Every Hausdorff topological vector space $E$ over $K$ , whose topology is defined by a set of semi-norms, is isomorphic to a sub-space of a product of Banach spaces.

If, further, the topology of $E$ is defined by an enumerable set of semi-norms, then $E$ is metrisable (I, p. 16).

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

Cited by

Nothing.

Cites

I, p. 16