×

zbMATH — the first resource for mathematics

Pervasive algebras on planar compacts. (English) Zbl 1010.46051
Let \(X\) be a compact Hausdorff space. A function algebra \(A\subset C(X)\) is called pervasive whenever for any non-void proper closed subset \(F\subset X\) the algebra of all restrictions \(\{f\mid F: f\in A\}\) is dense in \(C(F)\).
The author characterizes compact subsets \(X\) of the Riemann sphere \(S\) for which the algebra \(A(X)\) of all functions continuous on \(S\) and holomorphic on \(S\setminus X\), restricted to the set \(X\), is pervasive.
MSC:
46J10 Banach algebras of continuous functions, function algebras
30E10 Approximation in the complex plane
PDF BibTeX XML Cite
Full Text: EuDML