separability and completeness

Let $A = \{ a ? R^? \Bigg| \sum_{k=1}^{?} a_k= 0\}$. Determine whether $(A, d_?)$ is separable and whether it is complete

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

  • 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.

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