When the maximum ring of quotients of C(X) is uniformly complete

A Tychonoff space X such that the maximum ring of quotients of C(X) is uniformly complete is called a uniform quotients space. It is shown that this condition is equivalent to the Dedekind–MacNeille completion of C(X) being a ring of quotients of C(X), in the sense of Utumi. A compact metric space is a uniform quotients space precisely when it has a dense set of isolated points. Extremally disconnected spaces and almost P-spaces are uniform quotients spaces. Also characterized are the compact spaces of dense constancies which are uniform quotients spaces.