 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 Th63:
  for X be non empty TopSpace,T be NormedLinearTopSpace holds
  0.R_Normed_Space_of_C_0_Functions (X,T) = X --> 0.T
proof
  let X be non empty TopSpace,T be NormedLinearTopSpace;
  0.R_Normed_Space_of_C_0_Functions (X,T)
            =0.R_VectorSpace_of_C_0_Functions(X,T)
           .=X --> 0.T by Th62;
  hence thesis;
end;
