  Let $\cal A$ and $\cal B$ be two systems consisting of the same vector spaces
$\mathbb C^{n_1},\dots,\mathbb C^{n_t}$ and bilinear or sesquilinear forms
$A_i,B_i:\mathbb C^{n_{k(i)}}\times\mathbb C^{n_{l(i)}}\to\mathbb C$, for
$i=1,\dots,s$. We prove that $\cal A$ is transformed to $\cal B$ by
homeomorphisms within $\mathbb C^{n_1},\dots,\mathbb C^{n_t}$ if and only if
$\cal A$ is transformed to $\cal B$ by linear bijections within $\mathbb
C^{n_1},\dots,\mathbb C^{n_t}$.
