Compatible tight Riesz orders on C(X)

Abstract

AbstractThe pointwise order makes the group C(X) of continuous real-valued functions on a topological space X a lattice-ordered group. We give a characterization of the compatible tight Riesz orders on C(X), and also of their maximal tangents, in terms of the zero-sets of X. The space of maximal tangents of a given compatible tight Riesz order T is studied, and consequently the concept of the T-radical of C(X) is introduced, the T-radical being the intersection of all the maximal tangents of T.