On Order - Convergence of Filters in a Riesz Spaces

Document Type : Research Paper

Authors

1 Department of Mathematics, College of Science, University of Basrah, Basrah, Iraq.

2 Department 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.

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References

[1]         F. Riesz, "Sur la d´ecomposition des op´erations lin´eaires", Atti del Congresso Internazionale dei Matematici, 3, 143 (1928).
 
[2]         L. V. Kantorovich, "Lineare halbgeordnete Raume", Mathematica Sbornik, 44(1), 121 (1937).
 
[3]         H. Freudenthal, "Teilweise geordnete Moduln", Nederlandse Akademie Proceedings,   Series Mathematical Sciences, 39, 641 (1936).
 
[4]        C. D.  Aliprantis and O. Burkinshaw, "Locally Solid Riesz Spaces with Applications to Economics", Math Surveys and Monographs, American Math. Society, 105, 1 (2003).
 
[5]        D. Candeloro and A. R. Sambucini, "Filter Convergence and Decompositions for Vector Lattice- Valued Measures". Mediterranean Journal of Mathematics, 12, 621 (2015).
 
[6]        Sh. A. Kadhum and S. A. Kadhum, "Order-Convergence for Filters in a Dedekind Complete Riesz Spaces (K-Spaces)".Journal of physics: conference series, 1294, 1 (2019).
 
[7]        A. W. Wickstead, "Vector and Banach lattices", Mathematical Berlin Universitat, 85, 61 (2012).
 
[8]        D. C. Kent, "On the Order Topology in a Lattice", Illinois Journal of Mathematics, 10(1), 90 (1966).
 
M. Erné and S. Weck, "Order Convergence in lattices", Rocky Mountain Journal of Mathematics, 10(4), 805 (1980).
Kirkuk Journal of Science
Volume 15, Issue 2
June 2020
Page 17-24

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History

  • Receive Date: 30 November 1999
  • Accept Date: 11 July 2020

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