, Volume 15, Issue 1, pp 73-85
Date: 12 Jan 2010

On discrete and continuous quotient Riesz spaces

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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.

This research was partially supported by The Ministry of Science and Higher Education, Poland, Grant no. N N 201 2740 33.