Let $\varphi:G\rightarrow H$ be a continuous homomorphism between topological groups $G$ and $H$ and assume that $\ker \varphi $ is finite. Let $K<G$ be a closed subgroup. How to show that $Im (K)$ is closed subgroup of $H$?
2026-04-01 20:30:54.1775075454
The image of a closed subgroup is closed when the kernel is finite
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