A note on automatic continuity
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2017
- arXiv:
- arXiv:1710.04787
- Bibcode:
- 2017arXiv171004787C
- Keywords:
-
- Mathematics - Group Theory;
- 03E75;
- 54H11;
- 20E06
- E-Print:
- Proc. Amer. Math. Soc. 147 (2019), 1255-1268