  It is shown that if $A$ is a unital commutative Banach algebra with a dense
set of invertible elements, then the maximal ideal space of $A$ contains no
compact, locally connected, simply coconnected subspace of topological
dimension $\geq 2$. As a consequence, the existence of a compact set in
${\mathbb C}^2$ with a nontrivial polynomial hull that contains no topological
discs is obtained. This strengthens the celebrated result of Stolzenberg from
1963 that there exists a nontrivial polynomial hull that contains no analytic
discs, and it answers a question stated in the literature 10 years ago by Dales
and Feinstein but considered much earlier.
