Geodesic
A characterization of essential sets of function algebras
Archivum mathematicum, Tome 40 (2004) no. 3, pp. 229-232.

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In the present note, we characterize the essential set $E$ of a function algebra $A$ defined on a compact Hausdorff space $X$ in terms of local properties of functions in $A$ at the points off $E$.
Classification : 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); measure orthogonal to a function algebra 
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     author = {\v{C}erych, Jan},
     title = {A characterization of essential sets of function algebras},
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Čerych, Jan. A characterization of essential sets of function algebras. Archivum mathematicum, Tome 40 (2004) no. 3, pp. 229-232. http://geodesic.mathdoc.fr/item/ARM_2004__40_3_a1/