  Rosay and Rudin constructed examples of discrete subsets of C^n with
remarkable properties. We generalize these constructions from C^n to arbitrary
Stein manifolds. We prove: Given a Stein manifold X and a affine variety V of
the same dimension there exists a discrete subset D in X such that (1) X-D is
measure hyperbolic, (2) f(V) intersects D for every non-degenerate holomorphic
map from V to X and (3) every automorphism of X preserving the set D is already
the identity map. We also give examples which demonstrate that such discrete
subsets can not be found in arbitrary non-Stein manifolds.
