A note on rings of continous functions - J. S. Yang (International Journal of Mathematics and Mathematical Sciences)
For a topological space X, and a topological ring A, let C(X,A) be the ring of all continuous functions from X into A under the pointwise multiplication. We show that the theorem there is a completely regular space Y associated with a given topological space X such that C(Y,R) is isomorphic to C(X,R) may be extended to a fairly large class of topologlcal rings, and that, in the study of algebraic structure of the ring C(X,A), it is sufficient to study C(X,R) if A is path connected.