Let $G$ be a Hausdorff topological group with center $Z$ and closed subgroup $H$. Suppose that $H.Z = G$. Is the product map
$$H \times Z \rightarrow G$$
necessarily an open map? That is, can we identify with $G$ as a quotient group of $H \times Z$?
2026-03-24 22:07:46.1774390066
If $H$ and $Z$ are closed subgroups generating $G$, is $H \times Z \rightarrow G$ an open map?
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