  We prove results about limits of simple closed curves and polynomial hulls.
The results show, in particular, that the polynomially convex, rectifiable
simple closed curves in ${\mathbb C}^n$, $n\geq2$, form a dense open subset in
the space of all rectifiable simple closed curves with respect to both the
supremum norm and the total variation norm. Also, under suitable hypotheses,
the polynomial hull of the limit of a sequence of simple closed curves is the
limit of the polynomial hulls.
