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Examples are constructed that include, for n > m > 2, proper surjective maps f: Rn -* Rm that are one to one over the image of a dense subset D C Rn; i.e., the restriction of f yields a homeomorphism from f-If(D) onto f (D). A routine Baire Category argument establishes that, for any acompact subset F C Rn which f maps onto Rm, Int(F) #& 0 and, hence,

Mappings between Euclidean spaces that are one-to-one over the image of a dense subset