On discrete and continuous quotient Riesz spaces

On discrete and continuous quotient Riesz spaces Order properties of quotient Riesz spaces E/N(f) by null ideals N(f) are investigated. We show relationships between properties of a Riesz space E and its order dual E ~ and properties of quotients E/N(f) where f runs over some subspaces of E ~. A characterization of metrizable locally convex topological Riesz spaces whose all quotients (by proper closed ideals) are discrete is also given. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

On discrete and continuous quotient Riesz spaces

Positivity , Volume 15 (1) – Jan 12, 2010
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Publisher
SP Birkhäuser Verlag Basel
Copyright
Copyright © 2010 by Birkhäuser Verlag Basel/Switzerland
Subject
Mathematics; Econometrics; Operator Theory; Calculus of Variations and Optimal Control; Optimization; Fourier Analysis; Potential Theory
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-009-0042-3
Publisher site
See Article on Publisher Site

Abstract

Order properties of quotient Riesz spaces E/N(f) by null ideals N(f) are investigated. We show relationships between properties of a Riesz space E and its order dual E ~ and properties of quotients E/N(f) where f runs over some subspaces of E ~. A characterization of metrizable locally convex topological Riesz spaces whose all quotients (by proper closed ideals) are discrete is also given.

Journal

PositivitySpringer Journals

Published: Jan 12, 2010

References

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