Partial properness and real planar maps Original Research Article

If a local homeomorphism of the real plane, View the MathML source, is not one-to-one, then both f and g have fibers with connected components whose images under h are disjoint. Global homeomorphisms h are characterized in terms of properness along fibers of, and simplicity of, component maps. Two known counterexamples to univalence conjectures (for Samuelson maps and polynomial maps) are used to illustrate the results.