Abstract
Let X be a topological space, \({\mathfrak{S}}\) a cover of X and \({C_{b}(X, \mathbb{K};\mathfrak{S})}\) the algebra of all \({\mathbb{K}}\)-valued continuous functions on X which are bounded on every \({S \in \mathfrak{S}}\). A description of all closed (in particular, all closed maximal) ideals of \({C_{b}(X,\mathbb{K};\mathfrak{S})}\) is given with respect to the topology of \({\mathfrak{S}}\)-convergence and to the \({\mathfrak{S}}\)-strict topology.
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Research is in part supported by Estonian Science Foundation grant 6205.
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Abel, M., Arhippainen, J. & Kauppi, J. Description of Closed Ideals in Function Algebras Containing Continuous Unbounded Functions. Mediterr. J. Math. 7, 271–282 (2010). https://doi.org/10.1007/s00009-010-0035-2
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DOI: https://doi.org/10.1007/s00009-010-0035-2