  Given a compact $n$-dimensional immersed Riemannian manifold $M^n$ in some
Euclidean space we prove that if the Hausdorff dimension of the singular set of
the Gauss map is small, then $M^n$ is homeomorphic to the sphere $S^n$.
  Also, we define a concept of finite geometrical type and prove that finite
geometrical type hypersurfaces with small set of points of zero Gauss-Kronecker
curvature are topologically the sphere minus a finite number of points. A
characterization of the $2n$-catenoid is obtained.
