Positivity

, Volume 15, Issue 1, pp 73–85

On discrete and continuous quotient Riesz spaces

Article

DOI: 10.1007/s11117-009-0042-3

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

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 spaceBanach latticeLocally solid Riesz spaceNull idealOrder bounded operator

Mathematics Subject Classification (2000)

46A4046B4246B45

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2010

Authors and Affiliations

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