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Locally injective maps in o-minimal structures without poles are surjective

If f: R' is continuous and locally injective, then f is in fact surjective and a homeomorphism, provided f is definable in an o-minimal expansion without poles of the ordered additive group of real numbers; 'without poles' means that every one-variable definable function is locally bounded. Some general properties of definable maps in o-minimal expansions of ordered abelian groups without poles are also established.