A characterization of rings of density continuous functions (Q2497010)

Density continuous functions are defined to be the continuous functions mapping a Tikhonov\-space into the real line equipped with the density topology. The focus of this paper is the investigation when the family \(C(X,\mathbb R_{d})\) of all density continuous functions is a ring. It is shown that \(C(X,\mathbb R_{d})\) is a ring if each density continuous function is locally constant and in this case \(X\) is defined to be a density \(P\)-space. Moreover, the author gives some examples of \(P\)-spaces.