Functional representation of vector lattices. II (Q1337761)

An Archimedean vector lattice with weak order unit may be represented as a lattice of densely finite continuous real-valued functions on the compact space of its maximal ideals. This specializes to both the Banach lattice representation of [\textit{H. H. Schaefer}, `Banach lattices and positive operators', Berlin-Heidelberg-New York (1974; Zbl 0296.47023), III 4.5] and to that over the extremally disconnected Stone space of the complemented bands [\textit{W. A. J. Luxemburg} and \textit{A. C. Zaanen}, `Riesz spaces. I.', Amsterdam-London (1971; Zbl 0231.46014), 50.1, \textit{B. Z. Vulikh}, `Introduction to the theory of partially ordered vector spaces', Groningen (1967; Zbl 0186.446), V4.1]. [For part I see Proc. Am. Math. Soc. 108, No. 2, 471-478 (1990; Zbl 0743.46005)].