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Riesz spaces with the order-continuity property. I

Published online by Cambridge University Press:  24 October 2008

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

A Riesz space E has the (sequential) order-continuity property if every positive linear map from E to an Archimedean Riesz space is (sequentially) order-continuous. This is the case if and only if the canonical maps from E to its Archimedean quotient spaces are all (sequentially) order-continuous. I relate these properties to others that have been described elsewhere.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 81 , Issue 1 , January 1977 , pp. 31 - 42
Copyright
Copyright © Cambridge Philosophical Society 1977

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References

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