Example 3

Tag 02D5, permanent. Cite it as [Bourbaki, Tag 02D5].

Théories spectrales, chapter I, § 6. Algèbres stellaires

Let X be a compact topological space and let $x_0\in X$ be a fixed element of X. The subalgebra $\mathscr{C}'(X)$ of $\mathscr{C}(X)$ consisting of continuous functions $f: X\rightarrow$ $\mathbf{C}$ such that $f(x_0) = 0$ is a stellar algebra.

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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