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As is known (see Kadison-Ringrose, 3.4.1) each closed ideal $ I$ in the $ C^*$ -algebra $ C(X)$ of continuous functions on a compact space $ X$ has the form $ $ I=\{f\in C(X): \ \forall x\in S\quad f(x)=0 \} $ $ for some closed subset $ S$ in $ X$ . Is the sameRead more