  We construct a generalization of the Dolbeault-Grothendieck resolution on a
singular complex space. The same construction yields, for each morphism of
analytic spaces, a pullback mapping between the respective
Dolbeault-Grothendieck resolutions. As in the smooth case, the terms of the
resolution are soft sheaves with stalks which are flat with respect to the
sheaf of holomorphic sections. If, moreover, the complex space
$(X,\mathcal{O}_{X})$ is countable at infinity then the global section spaces
of the terms of the resolution are endowed with natural Fr\'{e}chet-Schwarz
topologies which induce the natural topology on the cohomology groups
$H^{\bullet }(X,\mathcal{O}_{X})$. The construction is an exercise in
globalization using semi-simplicial techniques. Using the above construction
one can produce, for instance, a soft resolution with $\mathcal{O}_{X}$-flat
stalks for the de Rham complex on the analytic space $X$.
