It is shown that a certain
simple imbedding T of the ordinary two-dimensional torus in C2 contains a
polynomially convex compact T-neighborhood of each of its points, but T is not
holomorphically convex in even the weakest presently accepted sense. This example
illustrates some of the limitations of a theory of lower dimensional sets in Cn.
In particular, it shows the difficulty of developing a theory based on local
information.