I am new to algebraic geometry. My question is simple, as title suggests it's about a grothendieck theorem. I mean, I don't understand what the statement of theorem exactly is. For simplicity of my understanding I have used the case of 1 variable.
I understand that theorem as follows:- If K[x] is a ring of polynomials in one variable and K is an algebraically closed field then if for all f belongs to K[x] is one to one then it's onto.
I understood it in this way and suspect many mistakes in it. Correct me by notifying the mistakes and also I have another question. How can some function be one to one and onto at the same time. So I also request an example clarifying my question