Hausdorff Dimension of Cantor Sets and Polynomial Hulls

  title={Hausdorff Dimension of Cantor Sets and Polynomial Hulls},
  author={Burglind J{\"O}RICKE}
  • Burglind JÖRICKE
We give examples of Cantor sets in C of Hausdorff dimension 1 whose polynomial hulls have non-empty interior. In the 60’ies W. Rudin [R] posed the following problem which arose in connection with Banach algebras and polynomial approximation. How small can the dimension of a compact subset K ofC be, provided its polynomial hull K̂ has non-empty interior. Asking about topological dimension, Vitushkin [V] and Henkin [H] constructed Cantor sets E in C2 with the latter property. Note that Cantor… CONTINUE READING