  Recently, it has been shown that multi-terminal superconducting
nanostructures may possess topological properties that involve Berry curvatures
in the parametric space of the superconducting phases of the terminals, and
associated Chern numbers that are manifested in quantized transconductances of
the nanostructure. In this Article, we investigate how the continuous spectrum
that is intrinsically present in superconductors, affects these properties. We
model the nanostructure within scattering formalism deriving the action and the
response function that permits a re-definition of Berry curvature for
continuous spectrum.
  We have found that the re-defined Berry curvature may have a non-topological
phase-independent contribution that adds a non-quantized part to the
transconductances. This contribution vanishes for a time-reversible scattering
matrix. We have found compact expressions for the redefined Berry curvature for
the cases of weak energy dependence of the scattering matrix and investigated
the vicinity of Weyl singularities in the spectrum.
