The Furstenberg structure theorem
Robert Richmond Ellis · Pacific Journal of Mathematics · 1978
The Furstenberg structure theorem for minimal distal flows is proved without any countability assumptions.Thus let (X, T) be a distal flow with compact Ήausdorff phase space X and phase group T. Then there exists an ordinal v and a family of flows (XJαrgv) such that X o is the one point flow, X»~X, X a+1 is an almost periodic extension of X a9 and Xβ=\im a< β Xr for all ordinals a and limit ordinals β less than or equal to v.