Let (X, d) be a compact metric space and let A ⊆ C(X; C) = {f : X → C; f is continuous} be an algebra that separates points and vanishes at no point in X. Assume additionally that A is self-adjoint, that is, for every f ∈ A, its complex conjugate f¯ is also in A. Show that A is dense in C(X; C).

Q: Q7: Prove that (R", |l-|| ) is complete metric space.

A: This is a problem of Topology, Functional Analysis.

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A: PROOF :

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A: Below given clear explanation

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A: Theorem: Proof:

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