Functional representation of vector lattices II
Copyright policy )Functional representation of vector lattices II
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)].
- University of Waterloo Canada
Topological representations of algebraic systems, Lattices of continuous, differentiable or analytic functions, Real-valued functions in general topology, complemented bands, Archimedean vector lattice, weak order unit, Ordered abelian groups, Riesz groups, ordered linear spaces, extremally disconnected Stone space, Ordered topological linear spaces, vector lattices
Topological representations of algebraic systems, Lattices of continuous, differentiable or analytic functions, Real-valued functions in general topology, complemented bands, Archimedean vector lattice, weak order unit, Ordered abelian groups, Riesz groups, ordered linear spaces, extremally disconnected Stone space, Ordered topological linear spaces, vector lattices
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