Let $A$ be a unital complex Banach algebra, and let $\Delta(A)$ denote the set of nonzero multiplicative complex-linear functionals $\tau:A\to\mathbb C$, viewed as a subspace of $A^*$ with the weak-* topology $\sigma(A^*,A)$. Then $\Delta(A)$ is a compact [Hausdorff space](/page/Hausdorff%20Space).