, Volume 15, Issue 1, pp 73–85

On discrete and continuous quotient Riesz spaces


DOI: 10.1007/s11117-009-0042-3

Cite this article as:
Wnuk, W. Positivity (2011) 15: 73. doi:10.1007/s11117-009-0042-3


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.


Riesz spaceBanach latticeLocally solid Riesz spaceNull idealOrder bounded operator

Mathematics Subject Classification (2000)


Copyright information

© Birkhäuser Verlag Basel/Switzerland 2010

Authors and Affiliations

  1. 1.Faculty of Mathematics and Computer ScienceA. Mickiewicz UniversityPoznanPoland