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A characterization of essential sets of function algebras

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*Jan Cerych*

**Address.**

Charles Univerity in Prague, Faculty of Mathematics and
Physics, Sokolovska 83, 186 00 Praha 8, Czech Republic

**E-mail. **

**Abstract.**

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 $E$.

**AMSclassification. **46J10.

**Keywords. **Compact Hausdorff space $X$, the sup-norm algebra $C(X)$ of all
complex-valued continuous f`unctions on $X$, its closed
subalgebras (called function algebras),
measure orthogonal to a function algebra.