A note on automatic continuity

@article{Conner2018ANO,
  title={A note on automatic continuity},
  author={Gregory R. Conner and Samuel M. Corson},
  journal={Proceedings of the American Mathematical Society},
  year={2018}
}
We present new results regarding automatic continuity, unifying some diagonalization concepts that have been developed over the years. For example, any homomorphism from a completely metrizable topological group to Thompson's group $F$ has open kernel. A similar claim holds when $F$ is replaced with a Baumslag-Solitar group or a torsion-free word hyperbolic group. 
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