A note on automatic continuity
Copyright policy )A note on automatic continuity
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.
- Brigham Young University Idaho United States
- University of the Basque Country Spain
Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations, completely metrizable group, Word problems, other decision problems, connections with logic and automata (group-theoretic aspects), word hyperbolic group, Group Theory (math.GR), slender group, Hyperbolic groups and nonpositively curved groups, locally compact Hausdorff group, 03E75, 54H11, 20E06, FOS: Mathematics, Geometric group theory, Thompson's group, Mathematics - Group Theory, Other groups related to topology or analysis, Topological groups (topological aspects)
Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations, completely metrizable group, Word problems, other decision problems, connections with logic and automata (group-theoretic aspects), word hyperbolic group, Group Theory (math.GR), slender group, Hyperbolic groups and nonpositively curved groups, locally compact Hausdorff group, 03E75, 54H11, 20E06, FOS: Mathematics, Geometric group theory, Thompson's group, Mathematics - Group Theory, Other groups related to topology or analysis, Topological groups (topological aspects)
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