  We construct an appropriate metric on the collection of piecewise $\mathcal
C^r$ maps defined on a compact interval. Although this metric space turns out
to be not complete, we show that it is indeed a Baire space. As an application,
we prove the robustness of non-degenerate critical points for this class of
systems and we show the genericity of piecewise Lipschitz maps that admit an
invariant Borel probability measure.
