  Surfaces of finite geometric type are complete, immersed into the
tree-dimensional Euclidean space with finite total curvature and Gauss map
extending to an oriented compact surface as a smooth branched covering map over
the unit sphere of the Euclidean three dimensional space. In a recent preprint
J. Jorge and F. Mercuri gave a geometric proof that the Gauss map can not omit
three or more points if the immersion is minimal and no flat. Here we give a
topological proof of this result in the class of no flat finite geometric type
surfaces and also give a topological classification when the Gauss map is a
regular covering map. This facts are easy applications of our main result, a
generalization of the little Picard theorem for the class of branched covering
of a finite geometric type surface into the unit sphere of the tree dimensional
Euclidean space. A finite geometric type surface given by a compact surface
minus a finite set of points has the following property: any branched covering
from the 0surface to the unit Euclidean sphere having a C extension to the
compact surfaces can miss at most 2 points. This is a generalization of the
little Picard theorem to the class of finite geometric type surfaces.
