Positivity

, Volume 15, Issue 1, pp 73–85

On discrete and continuous quotient Riesz spaces

Authors

    • Faculty of Mathematics and Computer ScienceA. Mickiewicz University
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 space Banach lattice Locally solid Riesz space Null ideal Order bounded operator

Mathematics Subject Classification (2000)

46A40 46B42 46B45

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2010