For broad classes of minimal group actions, almost every fiber of the maximal equicontinuous factor is an IT-set, which resolves two conjectures and links mean sensitivity to independence.
Auslander, A group theoretic condition in topological dynamics , Proceedings of the 18th Summer Conference on Topology and its Applications
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Independence and mean sensitivity in minimal systems under group actions
For broad classes of minimal group actions, almost every fiber of the maximal equicontinuous factor is an IT-set, which resolves two conjectures and links mean sensitivity to independence.