## Jan \v Cerych

*Pervasive algebras on planar compacts *

Comment.Math.Univ.Carolinae 40,3 (1999) 491-494. **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

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