
theorem Th44:
  for X be non empty TopSpace holds
  0.C_VectorSpace_of_C_0_Functions X = X --> 0
proof
  let X be non empty TopSpace;
A1: C_VectorSpace_of_C_0_Functions X is
    Subspace of ComplexVectSpace(the carrier of X) by Th41;
  0.ComplexVectSpace(the carrier of X) = X -->0;
  hence thesis by A1,CLVECT_1:30;
end;
