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Topological Completeness of Order Intervals in Riesz Spaces

Published online by Cambridge University Press:  20 November 2018

P. G. Dodds
P. G. Dodds*
Affiliation:
School of Mathematical Sciences, The Flinders University of South Australia, Bedford Park, S.A. 5042, Australia
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Abstract

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It is shown that if L is a Dedekind complete Riesz space equipped with a locally solid topology T defined by strongly (A, 0) Riesz pseudonorms, then order intervals of L are T-complete. This is an extension of a well known theorem of Nakano. The second part of the paper gives a necessary and sufficient condition for topological completeness of order intervals in a Dedekind σ-complete Riesz space which has a weak order unit and which is equipped with a locally solid σ-Fatou topology.

Keywords

46A4046A05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 3 , 01 September 1984 , pp. 316 - 323
Copyright
Copyright © Canadian Mathematical Society 1984

References

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