### An example of a Fréchet algebra which is a principal ideal domain

We construct an example of a Fréchet m-convex algebra which is a principal ideal domain, and has the unit disk as the maximal ideal space.

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We construct an example of a Fréchet m-convex algebra which is a principal ideal domain, and has the unit disk as the maximal ideal space.

Let $K\subseteq \u2102$ be a perfect compact set, $E$ a quasi-complete locally convex space over $\u2102$ and $f:K\to E$ a map. In this note we give a necessary and sufficient condition — in terms of differential quotients — for $f$ to have a holomorphic extension on a neighborhood of $K$.

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