×

Stone-Weierstrass type theorems for algebras containing continuous unbounded functions. (English) Zbl 1198.46025

Let \(X\) be a topological space and \(\sigma\) a cover (not necessarily open). The authors consider the question when a subalgebra of \(C_b(X,{\mathbb K},\sigma)\) is dense in this algebra in some topology (they consider here the topology of \(\sigma\)-convergence, the strict topology, or the \(\sigma\)-strict topology). The symbol \(C_b(X,{\mathbb K},\sigma)\) denotes the algebra of all \({\mathbb K}\)-valued functions continuous on \(X\) and bounded on each \(S\) in \(\sigma\), where \({\mathbb K}\) is \({\mathbb C}\) or \({\mathbb R}\). Several necessary and sufficient conditions are given. The authors also consider the question when the space \(C_b(X,{\mathbb K},\sigma)\) is complete.

MSC:

46E25 Rings and algebras of continuous, differentiable or analytic functions
46H05 General theory of topological algebras
PDFBibTeX XMLCite
Full Text: Link