Topological classification of systems of bilinear and sesquilinear forms

Let A and B be two systems consisting of the same vector spaces Cn1,…,Cnt and bilinear or sesquilinear forms Ai,Bi:Cnk(i)×Cnl(i)→C, for i=1,…,s. We prove that A is transformed to B by homeomorphisms within Cn1,…,Cnt if and only if A is transformed to B by linear bijections within Cn1,…,Cnt.