  A signature changing spacetime is one where an initially Riemannian manifold
with Euclidean signature evolves into the Lorentzian universe we see today.
This concept is motivated by problems in causality implied by the isotropy and
homogeneity of the universe. As initially time and space are indistinguishable
in signature change, these problems are removed. There has been some dispute as
to the nature of the junction conditions across the signature change, and in
particular, whether or not the metric is continuous there. We determine to what
extent the Colombeau algebra of new generalised functions resolves this dispute
by analysing both types of signature change within its framework. A covariant
formulation of the Colombeau algebra is used, in which the usual properties of
the new generalised functions are extended. We find that the Colombeau algebra
is insufficient to preclude either continuous or discontinuous signature
change, and is also unable to settle the dispute over the nature of the
junction conditions.
