
theorem Th32:
  for X be non empty TopSpace holds
  0.R_VectorSpace_of_C_0_Functions(X) = X -->0
proof
  let X be non empty TopSpace;
A1:R_VectorSpace_of_C_0_Functions(X) is
    Subspace of RealVectSpace(the carrier of X) by RSSPACE:11;
  0.RealVectSpace(the carrier of X) = X -->0;
  hence thesis by A1,RLSUB_1:11;
end;
