A map f is one-to-one (or injective) if any point in the range of f has at most one pre-image. That is, if f (p) = f (q) implies p = q.

A map f is locally one-to-one if every point p of the domain of f has a neighborhood that is mapped one-to-one by f . That is, for every p in the domain of f there is an open neighbordhood U of p such that f restricted to U is injective.

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8/12/94 -- The Geometry Center