Remark 1

With the notation of prop. 8, if $p$ is a closed mapping, this is not necessarily so for $p'($cf. TG, I, p. 72, example). However, if the mapping $p$ is closed and if A is a subspace of B, the mapping $p_A:\overset{-1}{p}(A)\rightarrow A$ is closed (TG, I, p. 30, prop. 2, a)).