 Multiplication of functions gives the non-gaps a numerical semigroup structure, and an old question of Adolf Hurwitz asked for a characterization of the semigroups occurring.A new necessary condition was found by R.-O.Buchweitz in 1980 and he gave an example of a subsemigroup of the nonnegative integers with 16 gaps that does not occur as the semigroup of non-gaps at a point on a curve of genus 16 (see ).