Let U be a real normed space such that, for an finite-dimensional, real normed space X,U contains a subspace isometrically isomorphic to X. Prove that every (not necessarily closed) subspace V of U of finite codimension has the same property. (We call V of finite codimension if there exists a finite-dimensional subspace N of U such that V\plus{}N\equal{}U.)
A. Bosznay inductionabstract algebrareal analysisreal analysis unsolved