
theorem Th7:
  for X being non empty TopSpace holds
  1_R_Algebra_of_ContinuousFunctions(X) = X --> 1
proof
  let X be non empty TopSpace;
A1:R_Algebra_of_ContinuousFunctions(X)
    is Subalgebra of RAlgebra the carrier of X by C0SP1:6;
  1_RAlgebra the carrier of X = X --> 1;
  hence thesis by A1,C0SP1:8;
end;
