Example 6

Tag 09HC, permanent. Cite it as [Bourbaki, Tag 09HC].

Integration, chapter VII, § 3. Applications and examples

— Special linear group. The closed subgroups $T_1(n, K)$ and ${}^t(T(n, K)^*)$ of $\mathbf{GL}(n, K)$ have intersection $\{e\}$ . Thus the mapping $(M, N) \mapsto M \cdot N$ is a continuous bijection $\varphi$ of $T_1(n, K) \times {}^t(T(n, K)^*)$ onto a subset $\Omega$ of $\mathbf{GL}(n, K)$ .

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

Example 5, § 3

Cites

Nothing.