CHANGE OF BASIS FOR LATTICE-VALUED CONVERGENCE GROUPS

T. M. G. Ahsanullah () and Fawzi Al-Thukair ()
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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

New Mathematics and Natural Computation (NMNC), 2011, vol. 07, issue 03, 453-469

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.

Keywords: L-topology; L-filter space; L-neighborhood group; L-neighborhood topological group; L-generalized convergence group; Galois connection; category (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1142/S1793005711002013

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