On preservation of automatic continuity

  • Samuel M. CorsonEmail author
  • Ilya Kazachkov


A group G is called automatically continuous if any homomorphism from a completely metrizable or locally compact Hausdorff group to G has open kernel. In this paper, we study preservation of automatic continuity under group-theoretic constructions, focusing mainly on groups of size less than continuum. In particular, we consider group extensions and graph products. As a consequence, we establish automatic continuity of virtually poly-free groups, and hence of non-exceptional spherical Artin groups. On the other hand, we show that if G is automatically continuous, then so is any finitely generated residually G group, hence, for instance, all finitely generated residually free groups are automatically continuous.


Free group First order theory Braid group Slender Root extraction Limit group 

Mathematics Subject Classification

Primary 54H11 20E26 Secondary 20F36 20E05 



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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Matematika SailaUPV/EHULeioaSpain

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