SUFFICIENT CONDITIONS FOR A LOCAL HOMEOMORPHISM TO BE INJECTIVE

Let U be an open connected subset of R(n) whose closure, UBAR, is compact and whose boundary, partial derivative U, has only finitely many components. Assume f: UBAR --> R(n) is a continuous map such that f\U is a local homeomorphism (e.g. f\U has continuous partial derivatives and nonvanishing Jacobian). Under certain hypotheses on partial derivative U and f\partial derivative U, it is proved that f must map U homeomorphically onto its image.