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Keywords:
compact Hausdorff space $X$; the sup-norm algebra $C(X)$ of all complex-valued continuous functions on $X$; its closed subalgebras (called function algebras); pervasive algebras; the algebra $A(X)$ of all functions continuous on $\Bbb S$ and holomorphic on $\Bbb S\smallsetminus X$
compact Hausdorff space $X$; the sup-norm algebra $C(X)$ of all complex-valued continuous functions on $X$; its closed subalgebras (called function algebras); pervasive algebras; the algebra $A(X)$ of all functions continuous on $\Bbb S$ and holomorphic on $\Bbb S\smallsetminus X$
Summary:
We characterize compact sets $X$ in the Riemann sphere $\Bbb S$ not separating $\Bbb S$ for which the algebra $A(X)$ of all functions continuous on $\Bbb S$ and holomorphic on $\Bbb S\smallsetminus X$, restricted to the set $X$, is pervasive on $X$.
References:
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