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Change Of Basis For Lattice-Valued Convergence Groups

Author

Listed:
  • T. M. G. AHSANULLAH

    (Department of Mathematics, King Saud University, Riyadh 11451, Saudi Arabia)

  • FAWZI AL-THUKAIR

    (Department of Mathematics, King Saud University, Riyadh 11451, Saudi Arabia)

Abstract

Using the idea of changing thebasis-lattice, we investigate in this article the impact ofchange-of-basisto the notion of stratified lattice-valued generalized convergence group by the so-called functorial mechanism. We discuss here some of the subcategories of the category of stratified lattice-valued generalized convergence groups, such as, stratified lattice-valued Kent convergence groups, stratified lattice-valued limit groups, and look into the possible link between these objects with stratified lattice-valued neighborhood groups and stratified lattice-valued neighborhood topological groups when bases are changed. Moreover, with the help of the notion of stratified lattice-valued filter attributed to U. Höhle and A. Šostak, we introduce a category>HŠ-SL-FilGrp, of stratified lattice-valued filter groups, and study its relationship with other categories so far achieved in this paper.

Suggested Citation

  • T. M. G. Ahsanullah & Fawzi Al-Thukair, 2011. "Change Of Basis For Lattice-Valued Convergence Groups," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 7(03), pages 453-469.
    • Handle: RePEc:wsi:nmncxx:v:07:y:2011:i:03:n:s1793005711002013
    DOI: 10.1142/S1793005711002013
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