# Topology : Homomorphisms

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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 homomorphism.

See the attached file.

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##### Solution Summary

Homomorphisms are investigated. The solution is detailed and well presented (see attached file).

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