Computable Gelfand Duality

TL;DR

This paper develops a computable version of Gelfand Duality, linking computably compact metrizable spaces with computable unital commutative C*-algebras, enabling effective analysis of these structures.

Contribution

It introduces a computable framework for Gelfand Duality, bridging computable topology and operator algebras in a novel way.

Findings

Establishes a computable correspondence between spaces and algebras.

Provides effective methods for representing compact metrizable spaces.

Enables algorithmic analysis of C*-algebras via topological data.

Abstract

We establish a computable version of Gelfand Duality. Under this computable duality, computably compact presentations of metrizable spaces uniformly effectively correspond to computable presentations of unital commutative $C^*$ algebras.