Article

Positivity

, Volume 15, Issue 1, pp 73-85

On discrete and continuous quotient Riesz spaces

  • Witold WnukAffiliated withFaculty of Mathematics and Computer Science, A. Mickiewicz University Email author 

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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.

Keywords

Riesz space Banach lattice Locally solid Riesz space Null ideal Order bounded operator

Mathematics Subject Classification (2000)

46A40 46B42 46B45