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Q: Is there a topological group with the small index property that does not have automatic continuity?

Yann PeresseHere 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, $G$ has automatic continuity if every group homomorphism from $G$ to any separable topological ...

 

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