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Questions tagged [automatic-continuity]

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10 votes
1 answer
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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,...
Yann Peresse's user avatar
4 votes
0 answers
104 views

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 ...
Luke Elliott's user avatar