Pointfree prime representation of real Riesz maps

Abstract.

In classical topology it is proved, nonconstructively, that for a topological space X, every bounded Riesz map ϕ in C(X) is of the form ${\ifmmode\expandafter\hat\else\expandafter\^\fi{x}}$ for a point x ∈ X. In this paper our main objective is to give the pointfree version of this result. In fact, we constructively represent each real Riesz map on a compact frame M by prime elements.