ABSTRACT
Most of what was known about both topological and algebraic aspects of C(X) prior to 1960 is described masterfully by L. Gillman and M. Jerison, whose terminology and notation is used in this chapter. While many functinal analysts have been convinced that general topology provides a source of valuable tools, very few algebraists regard general topology as a subject of much value to them. This note is a plea to the many talented workers in general topology to pay more attention to algebraic applications. To carry out such a task, one must first learn how to characterize algebraically in terms of the ring C(X) various topological properties of the space X. There is no known purely algebraic translation of local connectedness. If X is pseudocompact, and then the local connectedness of X is characterized in terms of C(X), considered to be a normed linear lattice.
