POLYNOMIAL HULLS OF ARCS AND CURVES

It is shown that there exist arcs and simple closed curves in C-3 with nontrivial polynomial hulls that contain no analytic discs. It is also shown that in any bounded, connected Runge domain of holomorphy in C-N (N >= 2) there exist polynomially convex arcs and simple closed curves of almost full measure. These results, which strengthen earlier results of the author, are obtained as consequences of a general result about polynomial hulls of arcs and simple closed curves through compact, totally disconnected sets.