Openness of Bh[g]-vectors

Determine whether the set of Bh[g]-vectors in K^n, where K is either the real or complex numbers and a Bh[g]-vector is an n-dimensional vector whose associated n-element subset has at most g representations for every element as a sum of h not necessarily distinct elements, is open in K^n.

Background

For positive integers g and h, a subset A of an additive abelian semigroup is a Bh[g]-set if every element has at most g representations as a sum of h not necessarily distinct elements of A. When K is either R or C, an element of K^n is a Bh[g]-vector if its associated n-element subset of K is a Bh[g]-set.

The paper proves that the set of Bh-vectors is a dense open subset of K^n. Since every Bh-set is a Bh[g]-set, the set of Bh[g]-vectors is consequently dense in K^n. The unresolved issue is whether this larger set is also open.