Stone duality for Dedekind σ-complete ℓ-groups with order-unit

Building on the Goodearl–Handelman–Lawrence functional representation theorem, we provide a purely topological representation (specifically, a categorical duality) for a large class of Dedekind σ-complete ℓ-groups G with order-unit u, including all G where u has a finite index of nilpotence. Our duality is a far-reaching generalization of the well-known Stone duality between σ-complete boolean algebras and basically disconnected compact Hausdorff spaces.