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Riesz spaces with the order-continuity property. II

Published online by Cambridge University Press:  24 October 2008

D. H. Fremlin
D. H. Fremlin
Affiliation:
University of Essex, Colchester
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Extract

I continue to investigate Riesz spaces E with the property that every positive linear map from E to an Archimedean Riesz space is sequentially order-continuous. In order to give a criterion for the product of such spaces to be another, we are forced to investigate their internal structure, and to develop an ordinal hierarchy of such spaces.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 83 , Issue 2 , March 1978 , pp. 211 - 223
Copyright
Copyright © Cambridge Philosophical Society 1978

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References

REFERENCES

(1)Fremlin, D. H.Riesz spaces with the order-continuity property. I. Math. Proc. Cambridge Philos. Soc. 81 (1977), 31–42.CrossRefGoogle Scholar
(2)Fremlin, D. H. Riesz spaces with the order-continuity property. III. F.M.R.I. Report No. 90, University of Essex, Colchester, 1977.Google Scholar
(3)Luxemrurg, W. J. H. and Zaanen, A. C.Riesz spaces I (North-Holland, 1971).Google Scholar
(4)Tucker, C. T.Homomorphisms of Riesz spaces. Pacific J. Math. 55 (1974), 289–300.CrossRefGoogle Scholar