Geodesic
Relativized Weak Mixing of Uncountable Order
Canadian journal of mathematics, Tome 32 (1980) no. 3, pp. 559-566

Voir la notice de l'article provenant de la source Cambridge University Press

We show that if Y is a metric minimal flow and θ: Y→Z in an open homomorphism that has a section (i.e., a RIM), and if S(θ)= R(θ),then °YΩ contains a dense set of transitive points, where Ω is the first uncountable ordinalYΩ = П{Y:1 ≦ α < Ω and α not a limit ordinal}, and °YΩ = {y ∈ YΩ:θ(yα)= θ(yβ)for 1 ≦ α,β < Ω and α, β not limit ordinals}, S(θ) is the relativized equicontinuous structure relation, and R(θ)= {(y1,y2) ∈ Y X Y:θ(y1) = θ(y2)}.We use this to generalize a result of Glasner that a metric minimal flow whose enveloping semigroup contains finitely many minimal ideals is PI, [5].I would like to thank Professor T. S. Wu for making helpful suggestions, and thank the referee for his time and effort. 
McMahon, Douglas. Relativized Weak Mixing of Uncountable Order. Canadian journal of mathematics, Tome 32 (1980) no. 3, pp. 559-566. doi: 10.4153/CJM-1980-042-4
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