Generalized Functions play a central role in the understanding of
differential equations containing singularities and nonlinearities. Introducing
infinitesimals and infinities to deal with these obstructions leads to
controversies concerning the existence, rigor and the amount of non-standard
analysis needed to understand these theories. Milieus constructed over the
generalized reals sidestep them all. A Riemannian manifold M embeds discretely
into a generalized manifold Mβ on which singularities vanish and products of
nonlinearities make sense. Linking this to an already existing global theory
provides an algebra embedding ΞΊ:G^β(M)βΆCβ(Mβ,Rfβ). Generalized Space-Time is
constructed and its possible effects on Classical Space-Time are examined