On Order - Convergence of Filters in a Riesz Spaces

Kadhim, Shatha Abdul-Hussein; Kadhim, Shaimaa Abdul-Hussein

doi:10.32894/kujss.2020.15.2.2

	On Order - Convergence of Filters in a Riesz Spaces
Kirkuk Journal of Science
Article 2, Volume 15, Issue 2, 2020, Pages 17-24 PDF (845.91 K)
Document Type: Research Paper
DOI: 10.32894/kujss.2020.15.2.2
Authors
Shatha Abdul-Hussein Kadhim^* ¹; Shaimaa Abdul-Hussein Kadhim²
¹Department of Mathematics, College of Science, University of Basrah, Basrah, Iraq.
²Department of Mathematics, College of Education for Pure Sciences. University of Basrah, Basrah. Iraq.
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

References
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