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Change Of Basis For Lattice-Valued Convergence Groups

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Author Info

  • 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)

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    Abstract

    Using the idea of changing the basis-lattice, we investigate in this article the impact of change-of-basis to 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.

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    Bibliographic Info

    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal New Mathematics and Natural Computation.

    Volume (Year): 07 (2011)
    Issue (Month): 03 ()
    Pages: 453-469

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    Handle: RePEc:wsi:nmncxx:v:07:y:2011:i:03:p:453-469

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    Related research

    Keywords: L-topology; L-filter space; L-neighborhood group; L-neighborhood topological group; L-generalized convergence group; Galois connection; category;

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