Real-valued functions on flows

Abstract. We develop the flow analog of the classical Yosida ad-junction between spaces and archimedean lattice-ordered groups with strong unit. A product of this development is the flow coun-terpart of the classical compactification of a space. We charac-terize those flows which are compactifiable, i.e., dense subflows of a compact flow. Finally, we exhibit a duality between the com-pactifications of a given flow and the topologies on the monoid of actions. 1