Natural uniform algebra (source code)

= Natural uniform algebra
{title2=$\Phi_A=\{\delta_x:x\in K\}$}

A <uniform algebra> on $K$ is natural if every <character of an algebra> is evaluation at a point of $K$. The evaluation embedding then identifies its character space homeomorphically with $K$. A <natural uniform algebra> is characterized by the <finite-generator criterion for a natural uniform algebra>. In particular, $C(K)$ is natural; the <disk algebra> is natural when its underlying space is the closed disk.