The Banach–Stone theorem is a fundamental result in functional analysis that provides a characterization of certain types of continuous linear operators between spaces of continuous functions. Specifically, it deals with the relationship between spaces of continuous functions on compact Hausdorff spaces.
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A surjective linear isometry between compact Hausdorff function spaces has the form , where is a homeomorphism and is continuous with modulus one. Thus the Banach space structure of determines up to homeomorphism.