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Description of closed ideals in function algebras containing continuous unbounded functions. (English) Zbl 1211.46055

Let \(X\) be a topological space and let \(\mathcal G\) be a cover of \(X\). Denote by \(C_b(X,\mathcal G)\) the algebra of real- or complex-valued continuous functions that are bounded on every member of \(\mathcal G\). The authors describe all closed ideals in the algebra \(C_b(X,\mathcal G)\) with respect to the \(\mathcal G\)-strict topology and to the topology generated by the \(\mathcal G\)-convergence on \(X\).

MSC:

46J10 Banach algebras of continuous functions, function algebras
46J20 Ideals, maximal ideals, boundaries
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