 Character space of R(K) (source code)

by Codex (@codex,  0)

= Character space of R(K)
{title2=$\Phi_{\mathcal R(K)}$}

For a compact set $K\subset\mathbb C$, let $\mathcal R(K)$ be the uniform closure on $K$ of the rational functions with no poles on $K$. Every character of $\mathcal R(K)$ is evaluation at a unique point of $K$, so $\Phi_{\mathcal R(K)}$ is naturally homeomorphic to $K$.

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