The NIP Hausdorffness conjecture for Ellis groups
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.
Sources & referencesView supporting material
Primary source
Krzysztof Krupiński and Anand Pillay, “Generalized locally compact models for approximate groups”, arXiv:2310.20683 (2026).
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