A relationship between the order convergence and the relative uniform convergence in a Riesz space

Abstract

In this paper, we give a complete description of Riesz spaces where every positive increasing and bounded from above sequence converges relatively uniformly. A Riesz space with this property will be called a Dedekind u-complete Riesz space. The location of this concept in the main inclusion theorem of Luxemburg and Zaanen will be investigated.