 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 Th36:
  for S be non empty compact TopSpace,T be NormedLinearTopSpace
  for x be Point of R_NormSpace_of_ContinuousFunctions(S,T),
  y be Point of R_NormSpace_of_BoundedFunctions(the carrier of S,T)
    st x=y holds ||.x.||= ||.y.|| by FUNCT_1:49;
