= Character space of continuous functions on the circle
{title2=$\Phi_{C(\mathbb T)}\cong\mathbb T$}
A <maximal ideal> $M$ of $C(\mathbb T)$ has a common zero: otherwise finitely many $f_j\in M$ have no simultaneous zero, and $\sum_j|f_j|^2\in M$ is invertible, a contradiction. If the common zero is $z$, then $M$ is the kernel of evaluation at $z$ by maximality. Thus every <algebra character> is point evaluation. Continuous functions separate distinct points of the <unit circle>, and the evaluation bijection is a <homeomorphism> for the <Gelfand topology>.
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