Bourbaki

Remark 2

Tag 02O0, permanent. Cite it as [Bourbaki, Tag 02O0].

Théories spectrales, chapter III, § 1. Applications linéaires compactes

Let E be a seminormed space and let B be the unit ball of E. In order that a linear mapping uu from E into a separated topological vector space F be compact, it is necessary and sufficient that u(B)u(B) be a relatively compact subset of F.

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

Cited by

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Cites

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Machine translation of the English, by gpt-5-6-mini, gpt-5-mini, gpt-5.4, against glossary version 34. Not checked by a person. That model is a cut down version of the one the rest of this language was written by.