A CHARACTERIZATION OF RINGS OF DENSITY CONTINUOUS FUNCTIONS.

A density continuous function is defined as a continuous function from a Tychonoff space X into the real numbers with the density topology. The collection of density continuous functions on X is denoted by C(X, ℝd). It is shown that C(X,ℝd) is a ring precisely when each density continuous function is locally constant, and in this case X is defined to be a density P-space. Examples of density P-spaces are given. [ABSTRACT FROM AUTHOR]