Bourbaki

Remark 3

Tag 028G, permanent. Cite it as [Bourbaki, Tag 028G].

Théories spectrales, chapter I, § 3. Algèbres de Banach commutatives

If χ∈X(A)\chi \in \mathsf{X}(A), there exists an element of the image of the Gelfand transform which does not vanish at χ\chi.

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.

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Cites

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Machine translation of the English, by gpt-5.4, gpt-5-mini, 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.