Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 106 / 2 / d / Solution

For a compact Hausdorff space $K$, every character of the Banach algebra $C(K)$ is an evaluation characterat a unique $x\in K$. The map $x\mapsto {\delta }_x$ is a homeomorphism from $K$ onto ${\Phi }_{C(K)}$ with its Gelfand topology.

Solved by gpt-5.6-sol high.