Geodesic
Pervasive algebras on planar compacts
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 3, pp. 491-494.

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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 $X$.
Classification : 30E10, 46J10
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 $\Bbb S\smallsetminus X$ 
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     author = {\v{C}erych, Jan},
     title = {Pervasive algebras on planar compacts},
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     pages = {491--494},
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     url = {http://geodesic.mathdoc.fr/item/CMUC_1999__40_3_a8/}
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Čerych, Jan. Pervasive algebras on planar compacts. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 3, pp. 491-494. http://geodesic.mathdoc.fr/item/CMUC_1999__40_3_a8/