
theorem Th13:
  for X being non empty TopSpace holds
    0.(C_Algebra_of_ContinuousFunctions X) = X --> 0c
proof
  let X be non empty TopSpace;
A1:C_Algebra_of_ContinuousFunctions X
           is ComplexSubAlgebra of CAlgebra the carrier of X by CC0SP1:2;
  0.(CAlgebra the carrier of X) = X --> 0c;
  hence 0.(C_Algebra_of_ContinuousFunctions X) = X --> 0 by A1,CC0SP1:3;
end;
