 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 S,T be RealNormSpace holds RLSStruct (# ContinuousFunctions(S,T),
    Zero_(ContinuousFunctions(S,T),RealVectSpace(the carrier of S,T)),
    Add_(ContinuousFunctions(S,T),RealVectSpace(the carrier of S,T)),
    Mult_(ContinuousFunctions(S,T), RealVectSpace(the carrier of S,T))
      #) is Subspace of RealVectSpace(the carrier of S,T)
        by Th11,RSSPACE:11;
