 reserve
  S for non empty TopSpace,
  T for LinearTopSpace,
  X for non empty Subset of the carrier of S;
 reserve
    S,T for RealNormSpace,
    X for non empty Subset of the carrier of S;

theorem
  for X be non empty TopSpace,T be NormedLinearTopSpace holds
  R_VectorSpace_of_C_0_Functions(X,T)
  is Subspace of RealVectSpace(the carrier of X,T) by RSSPACE:11;
