Proposition 5

Tag 0BYD, permanent. Cite it as [Bourbaki, Tag 0BYD].

For every closed subgroup $G$ of $\mathbf{R}^n$ ,

r(G^*) = n - d(G) \quad \text{and} \quad d(G^*) = n - r(G).

Let us apply the same reasoning to

G^*

. Observing that the basis dual to

(a'_i)

(a_i)

, we see that:

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

Cited by

Nothing.