Abstract: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 $X$.
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 $\Bbb S\smallsetminus X$
AMS Subject Classification: 46J10, 30E10