  Let M be a manifold, possibly with boundary. We show that the deRham
differential from k-forms to exact (k+1)-forms has a continuous right inverse
when both spaces are given the weak Whitney topology. This antidifferential
operator is given a fairly explicit formula depending on the choice of a
suitable good cover of M and local coordinates on the elements of the cover. If
the antidifferential operator is applied to a smooth family of exact forms, it
produces a smooth family of forms.
