Topological f-rings.

In [1], Birkhoff and Pierce introduced the concept of f-ring. In (7], [9], and [10] it was shown that certain Archimedian f-rings can be represented as rings of continuous extended real valued functions on various topological spaces. It was noted that the m-topology on rings of continuous real valued functions (see problem 2N of [6]) could be generalized to arbitrary f-rings provided they were convex in the sense of [5]. It was also shown that every f-ring can be embedded in a smallest convex f-ring. [...