
theorem Th14:
  for X being non empty TopSpace holds
   1_(C_Algebra_of_ContinuousFunctions X) = X --> 1r
proof
  let X be non empty TopSpace;
A1:C_Algebra_of_ContinuousFunctions X
           is ComplexSubAlgebra of CAlgebra the carrier of X by CC0SP1:2;
  1_(CAlgebra the carrier of X) = X --> 1r;
  hence 1_(C_Algebra_of_ContinuousFunctions X) = X --> 1r by A1,CC0SP1:3;
end;
