On Order - Convergence of Filters in a Riesz Spaces

Abstract

The main purpose of  this paper, is study  the ideas of order- Convergence of filters in a Riesz spaces and that is through prove an important theorems related to the some properties Riesz spaces. So we established that the intersection and union all subsets of the collection of all proper filters  were converge to point in Riesz space it's the same convergence point the filter there exist in these subsets and proved that order-convergence for intersection (union) two filters to intersection (union) two different points in Riesz space is equivalent to the set consist of two convergence points we could write it by using these filters.

Keywords

• order - convergence for filter
• lattice
• riesz space