The NIP Hausdorffness conjecture for Ellis groups
Let be a first-order structure with NIP. Let be a group definable in , let be -saturated, and let be the Ellis group of the flow , equipped with its -topology.
NIP Hausdorffness conjecture. If has NIP, then is Hausdorff.
In general, non-Hausdorff Ellis groups are known, but the source reports no such example with NIP. Thus the assertion remains open in the stated generality.
References
Primary source
Krzysztof Krupiński and Anand Pillay, “Generalized locally compact models for approximate groups”, arXiv:2310.20683 (2026).
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