Evaluative presentations

Abstract We study presentations of $C(X)$ that are evaluative over a presentation of $X$ in that $(f,p) \mapsto f(p)$ is computable. We prove existence–uniqueness theorems for such presentations. We use our methods to prove an effective Banach–Stone Theorem for unital commutative $C^{*}$ algebras. We also apply our results to the computable categoricity of $C^{*}$ algebras and compact Polish spaces.