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Tagged with automatic-continuity topological-groups
2 questions
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Does the group of homeomorphisms of the hilbert cube have automatic continuity
A topological group is said to have automatic continuity if every homomorphism from it to a second countable topological group is continuous. Various topological groups are known to have this ...
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Is there a topological group with the small index property that does not have automatic continuity?
Here are the exact definitions of the terms:
Let $G$ be a topological group.
Then $G$ has the small index property if every subgroup of countable (including finite) index is open in $G$. Furthermore,...
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