# separability and completeness

Let $A = \{ f(x) = \sum_{k=1}^n c_kx^k \Bigg| n ∈ \mathbb{Z}^+, |c_k| ≤ 1$ for all $k\}$ $⊆ (C([0, 1], R), d_∞).$ Determine whether $(A, d∞)$ is separable and whether it is complete

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While these are standard facts writing out the details will take more time than the bounty is worth.

I second that. The offered bounty is too low.