
theorem Th45:
  for X be non empty TopSpace holds
  0.C_Normed_Space_of_C_0_Functions X = X --> 0
proof
  let X be non empty TopSpace;
  0.C_Normed_Space_of_C_0_Functions X
            =0.C_VectorSpace_of_C_0_Functions X
           .=X --> 0 by Th44;
  hence thesis;
end;
