Vol. 76, No. 2, 1978

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The Furstenberg structure theorem

Robert Ellis

Vol. 76 (1978), No. 2, 345–349
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 (Xα|α ν) such that X0 is the one point flow, Xν = X, Xα+1 is an almost periodic extension of Xα, and Xβ = lim
←−α<βXγ 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
Authors
Robert Ellis