  The main result is that, for any projective compact analytic subset A of
dimension q>0 in a reduced complex space X, there is a neighborhood U of A such
that, for any covering space Z of X in which the lifting B of A has no
noncompact connected analytic subsets of pure dimension q with only compact
irreducible components, there exists a smooth exhaustion function on Z which is
strongly q-convex on the lifting of U outside a uniform neighborhood of the
q-dimensional compact irreducible components B.
