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Free Vector Lattices

Published online by Cambridge University Press:  20 November 2018

Kirby A. Baker
Kirby A. Baker*
Affiliation:
Harvard University, Cambridge, Mass. and California Institute of Technology, Pasadena, Calif.
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 58 - 66
Copyright
Copyright © Canadian Mathematical Society 1968

Footnotes

*

The author is indebted to Professor Birkhoff for suggesting this application of his theorem. A similar application appears in Henrikson-Isbell (7, § 4).

References

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