Singularities in Space-time Foam Algebras

In this paper we consider the structure of the singularity sets associated with generalized functions in certain space-time foam algebras of generalized functions. In particular, we consider the algebra that is defined in terms of an asymptotic vanishing condition outside sets of first Baire category. It is shown that this algebra is in fact isomorphic to the earlier closed nowhere dense algebras. We also discuss general questions regarding singularities that can be handled in space-time foam algebras.