Let $(X, d)$ be a compact metric space. Is $C(X, \mathbb{C})$ separable? I've already checked an answer, but I think that my problem is that my continuous functions take value in $\mathbb{C}$. Does this change anything in separability? If not, can I follow the same proof or I have to change something?
2026-03-26 14:26:10.1774535170
$C(X, \mathbb{C})$ separable
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