Q1. Claim: Suppose f : Rn -> Rm is injective. Then m >= n. Is this true? Q2. Claim: Suppose f : Rn -> Rn is injective and f(X) = [f1(X) f2(X) ... fn(X)]T. Then each fk must be injective. Is this true? Q3. I assume the above claims are known results or have known counterexamples. Can someone direct me to a good text or reference for questions such as these? Thanks.