Year: 2026
Type: preprint
Abstract: We prove a general theorem giving constraints on maps from certain topological groups to inverse limits of bounded torsion groups. From this we obtain some automatic continuity and ultraproduct results. For example, every homomorphism from a Polish group to a countable torsion-free residually finite group has open kernel. Also, the Grigorchuk group is a homomorphic image of a nonprincipal ultraproduct of groups if and only if there exists a measurable cardinal.
Source: arXiv (Cornell University)
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7167220469
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