It is a well-known fact that on a bounded spectral interval the Dirac
spectrum can described locally by a non-decreasing sequence of continuous functions
of the Riemannian metric. In the present article we extend this result to a global
version. We think of the spectrum of a Dirac operator as a function Z ! R and
endow the space of all spectra with an arsinh-uniform metric. We prove that the
spectrum of the Dirac operator depends continuously on the Riemannian metric. As
a corollary, we obtain the existence of a non-decreasing family of functions on the
space of all Riemannian metrics, which represents the entire Dirac spectrum at any
metric. We also show that in general these functions do not descend to the space of
Riemannian metrics modulo spin di�eomorphisms due to spectral
ow.