Find two subgroups $G_1$ and $G_2$ of $GL(2,\mathbb{C})$, and an isomorphism $f:G_1\rightarrow G_2$ which fails to be a homeomorphism. The metric on $GL(2,\mathbb{C})$ is the induced metric from $\mathbb{C}^4$. This is an exercise in The Geometry of Discrete Groups. A hint would be appreciated.
2026-03-30 23:12:41.1774912361
Find two subgroups of $GL(2,\mathbb{C})$ and an isomorphism between them that is not a homeomorphism.
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