Homework Statement
1. Prove that if a metric space (X,d) is separable, then
(X,d) is second countable.2. Prove that \ell^2 is separable.
Homework Equations
The Attempt at a Solution
1. \{ x_1,\ldots,x_k,\ldots \} is countable dense subset. Index the
basis with rational numbers, \{ B(x,r) | x...