Bourbaki

Corollary 3

Tag 027W, permanent. Cite it as [Bourbaki, Tag 027W].

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

Suppose X compact. Then the mapping x↦x\mapsto evx_x is a homeomorphism of X onto X(C(X))\mathsf{X}(\mathscr{C}(X)). The weak topology and the Jacobson topology coincide on X(C(X))\mathsf{X}(\mathscr{C}(X)).

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

Nothing.

Cites

Nothing.

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.