I'm struggling with the proof of the following question:
Let (R^p,∥.∥) be a normed space. Prove that R^p is complete if and only if the set (S,∥.∥) is complete, where S = {x ̄ ∈ R^p : ∥x ̄∥ = 1}.
If anyone is willing to provide me with the proof I would really appreciate it.
Kind regards Layla