MathDB

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

U

of finite codimension has the same property. (We call

V

of finite codimension if there exists a finite-dimensional subspace

N

U

such that V\plus{}N\equal{}U.) A. Bosznay

Problem Statement