= Character space of C1 on a compact interval
{title2=$\Phi_{C^1[0,1]}=\{\delta_t:t\in[0,1]\}$}
The coordinate function has spectrum $[0,1]$: outside the interval its difference from a scalar has a continuously differentiable reciprocal, and on the interval it has a zero. Every <character of an algebra> therefore takes the coordinate to some $t\in[0,1]$. Polynomial density in the norm containing both function and derivative, together with <automatic continuity of characters>, forces evaluation at $t$ on every function. The <maximal ideals> are exactly $\{f:f(t)=0\}$.
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