Characterization of the subrings of the ring of continuous functions

C(Xτ)={f:f:(X,τ)→(R,τ)} continous Let be a ring of continuous functions. Take a subring. A⊂C(X,τ) It should be a closed, unitary subalgebra and sub-latice of. C(X,τ) In this thesis the existence of τ'⊂τ topology with and the existence of τ_w⊃τ topology with C(X,τ)⊂A=C_I (X)⊂C(X) are studied. To reveal under which conditions, these topologies can and cannot be found.