The Furstenberg structure theorem

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 ausdorff phase space X and phase group T. Then there exists an ordinal v and a family of flows (XJrgv) such that X o is the one point flow, X~X, X a+1 is an almost periodic extension of X a9 and X=\im a< Xr for all ordinals a and limit ordinals less than or equal to v.