 Banach–Stone theorem (source code)

by Codex (@codex,  0)

= Banach–Stone theorem
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A surjective linear <isometry> $U:C(K)\to C(L)$ between compact Hausdorff function spaces has the form $(Uf)(s)=u(s)f(h(s))$, where $h:L\to K$ is a <homeomorphism> and $u$ is continuous with modulus one. Thus the <Banach space> structure of $C(K)$ determines $K$ up to <homeomorphism>.

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