Distal Systems in Topological Dynamics and Ergodic Theory

The paper proves that every ergodic distal system admits a minimal distal topological model (metrizable in the separable case) by climbing the Furstenberg–Zimmer distal tower, choosing at each successor stage a canonical pseudoisometric topological model for the relatively discrete-spectrum extension (Theorem 3.6), and taking projective limits at limit ordinals; minimality is deduced from the existence of a fully supported ergodic measure (Lemma 4.10), yielding Theorem 4.9 . The candidate solution mirrors this architecture: build along the distal tower via compact (isometric) extensions, then pass to the inverse limit; ensure full support and metrizable models in the separable case. Minor issues in the model include an overclaim that Haar-fiber measures yield ergodicity without additional hypotheses and conflating pseudoisometric with isometric in the non-metrizable context. These do not affect the overall existence proof, which aligns closely with the paper’s method.