GLOBAL UNIVALENCE OF PARTIALLY PROPER LOCAL HOMEOMORPHISMS

A local homeomorphism (f, g) : N --> L x M of connected topological ma nifolds is shown to be one-to-one if it is one-to-one on certain compo nents of fibers f(-1)(u) and g(-1)(v), and satisfies a fiber overlap c ondition. This yields an analogue of Hadamard's theorem on proper loca l homeomorphisms that requires only partial properness (at the expense of an overlap condition).