The Furstenberg structure theorem

Robert Ellis

Vol. 76 (1978), No. 2, 345–349

DOI: 10.2140/pjm.1978.76.345

Abstract

The Furstenberg structure theorem for minimal distal flows is proved without any countability assumptions. Thus let (X,T) be a distal flow with compact Hausdorff phase space X and phase group T. Then there exists an ordinal ν and a family of flows (X_α|α ≦ ν) such that X₀ is the one point flow, X_ν = X, X_α+1 is an almost periodic extension of X_α, and X_β = _α<βX_γ for all ordinals α and limit ordinals β less than or equal to ν.

Mathematical Subject Classification 2000

Primary: 54H20

Milestones

Received: 13 April 1977

Revised: 20 October 1977

Published: 1 June 1978