Homomorphisms from topological groups to inverse limits

Gregory R. Conner; Samuel M. Corson; Curtis Kent

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arXiv · 2607.01411

Homomorphisms from topological groups to inverse limits

Gregory R. Conner·Samuel M. Corson·Curtis Kent

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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.

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BibTeX RIS

Gregory R. Conner, Samuel M. Corson, Curtis Kent. 2026-07-01. Homomorphisms from topological groups to inverse limits. https://arxiv.org/abs/2607.01411

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