Assignment:
Define f: [0, 1) → C by f (x) = e2πix. Prove that f is one-one, onto, and continuous. Find a point x ∈ [0, 1) and a neighborhood N of x in [0, 1) such that f (N) is not a neighborhood of f (x) in C. Deduce that f is not a homeomorphism.
Provide complete and step by step solution for the question and show calculations and use formulas.