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.
Positivity – Springer Journals
Published: Jan 12, 2010
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