Geodesic
Free Vector Lattices
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 58-66

Voir la notice de l'article provenant de la source Cambridge University Press

This note presents a useful explicit characterization of the free vector lattice FVL(א) on א generators as a vector lattice of piecewise linear, continuous functions on Rא, where א is any cardinal and R is the set of real numbers. A transfinite construction of FVL(א) has been given by Weinberg (14) and simplified by Holland (13, § 5). Weinberg's construction yields the fact that FVL(א) is semi-simple; the present characterization is obtained by combining this fact with a theorem from universal algebra due to Garrett Birkhoff. 
Baker, Kirby A. Free Vector Lattices. Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 58-66. doi: 10.4153/CJM-1968-008-x
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