A new proof of the odd number of images generated by a non-singular gravitational lens

In this paper we provide a new proof of a general theorem on
gravitational lenses, first shown by Burke (1981) for the special case of thin lenses.
The theorem states that a transparent gravitational lens with non-singular mass
distribution produces an odd number of images of a point source. Our general
proof shows that the topological and Brouwer’s degrees find natural and interesting
applications in the theory of gravitational lenses.