Corollary 1

Under the hypotheses of Prop. 3, two maximal totally isotropic (resp. totally singular) subspaces of finite dimension have the same dimension. For every maximal totally isotropic (resp. totally singular) subspace F of finite dimension, there exists another F' such that F ∩ F' = {0}, and under these conditions F + F' is non-isotropic.

If F ∩ F' = {0}, we shall have G = {0} with the notation of Prop. 3, and F + F' will be non-isotropic. The other assertions follow trivially from Prop. 3 and Cor. 1 of Prop. 2.