Solution
= Solution
The real <Stone-Weierstrass theorem> says that a real <subalgebra> $A\subset C(K,\mathbb R)$ which contains the constants and separates points is dense in $C(K,\mathbb R)$ for the <uniform norm>, when $K$ is <compact Hausdorff space>. If $A$ is also closed, \b[$A=C(K,\mathbb R)$]. The complex version needs closure under <complex conjugation>; that extra condition is unnecessary here.