Bourbaki

Remark 1

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

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

A neighbourhood of 0 in E absorbs every bounded subset of E; the image of a bounded subset of E by a compact linear mapping from E into F is therefore 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.