Evaluative presentations

Abstract

We study presentations of $C^{\ast }(X)$ 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 $C^{\ast }$ algebras. We also apply our results to the computable categoricity of $C^{\ast }$ algebras and compact Polish spaces.