ABSTRACT
Early work in rings of continuous functions displayed some algebraic flavor, as the words ought to suggest. Stone discussed basic properties of the ring C∗(X) for completely regular X and exploited these properties in conjunction with a certain Boolean ring of subsets of X to construct βX; a byproduct was the theorem that every residue class field of C∗(X) is the real field. These results are mostly in the nature of representation theorems, showing one-one correspondences between a pair of structures so that statements about either one have a natural translation in terms of the other. This type of theorem may tend to close off a subject rather than open it up. Other types of problems about C(X) have been tackled. Naturally, some of the results are scattered, while others stem from a concentrated investigation of a single topic or a concerted attack on a particular problem.
