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Representation of pseudo-lattice ordered vector spaces

Published online by Cambridge University Press:  09 April 2009

Richard C. Metzler
Richard C. Metzler
Affiliation:
Department of Mathematics University of New MexicoAlbuquerque, New Mexico 87131, U.S.A.
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Abstract

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Ordered vector spaces more general than vector lattices are represented as function spaces with ‘almost’ the pointwise order. The ‘pseudo-lattice’ property which is necessary (and sufficient in the finite-dimensional case) for the representation is also studied in relation to the lattice property.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 27 , Issue 2 , March 1979 , pp. 167 - 172
Copyright
Copyright © Australian Mathematical Society 1979

References

Jameson, G. (1970), Ordered linear spaces (Springer-Verlag, Berlin, 1970).CrossRefGoogle Scholar
Metzler, R. (1969), ‘Representation of ordered vector spaces with the Riesz decomposition property’, J. London Math. Soc. (2) 1, 3–10.CrossRefGoogle Scholar
Metzler, R. (1975), ‘Representation of ordered linear spaces’, Rocky Mountain J. Math. 5, 427–443.CrossRefGoogle Scholar