Geodesic
On the topological dimension of the essential boundary of polynomially convex domains
Izvestiya. Mathematics , Tome 10 (1976) no. 2, pp. 445-450

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We construct an example of a polynomially convex closed domain whose Shilov boundary is zero-dimensional. Bibliography: 4 titles. 
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     author = {S. N. Bychkov},
     title = {On the topological dimension of the essential boundary of polynomially convex domains},
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S. N. Bychkov. On the topological dimension of the essential boundary of polynomially convex domains. Izvestiya. Mathematics , Tome 10 (1976) no. 2, pp. 445-450. http://geodesic.mathdoc.fr/item/IM2_1976_10_2_a12/