The NIP Hausdorffness conjecture for Ellis groups

Let MM be a first-order structure with NIP. Let GG be a group definable in MM, let NMN\succ M be N+|N|^+-saturated, and let uMu\mathcal{M} be the Ellis group of the flow (G,SG,M(N))(G,S_{G,M}(N)), equipped with its τ\tau-topology.

NIP Hausdorffness conjecture. If MM has NIP, then uMu\mathcal{M} 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).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.