Abstract
We demonstrate that any surjective isometry T:A→B not assumed to be linear between unital, completely regular subspaces of complex-valued, continuous functions on compact Hausdorff spaces is of the form T(f)=T(0)+Re[μ⋅(f∘τ)]+iIm[ν⋅(f∘ρ)], where μ and ν are continuous and unimodular, there exists a clopen set K with ν=μ on K and ν=−μ on Kc, and τ and ρ are homeomorphisms.
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