Several results of Hahn-Vitali-Saks type are given for sequences in the order dual of an Archimedean Riesz space with separating order dual. The class of Riesz spaces considered contains those which are Dedekind ocomplete, or have the projection property or have an interpolation property introduced by G. L. Seever. The results depend on recent work of O. Burkinshaw and some results of uniform boundedness type.
- Archimedean Riesz spaces
- Order dual
- Principal projection property
- Sequential convergence
- Weak compactness