  For any compact set $K \subseteq \mathbb{R}^3$ we define a number $r(K)$ that
is either a nonnegative integer or $\infty$. Intuitively, $r(K)$ provides some
information on how wildly $K$ sits in $\mathbb{R}^3$. We show that attractors
for discrete or continuous dynamical systems have finite $r$ and then prove
that certain arcs, balls and spheres cannot be attractors by showing that their
$r$ is infinite.
