Description of closed ideals in function algebras containing continuous unbounded functions (Q711438)

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 \(X\).