On the Aspects of Enriched Lattice-valued Topological Groups and Closure of Lattice-valued Subgroups





lattice, topology, fuzzy topology, lattice-valued topology, lattice-valued subgroup, group, category


Starting with L as an enriched cl-premonoid, in this paper, we explore some categorical connections between L-valued topological groups and Kent convergence groups, where it is shown that every L-valued topological group determines a well-known Kent convergence group, and conversely, every Kent convergence group induces an L-valued topological group. Considering an L-valued subgroup of a group, we show that the category of L-valued groups, L-GRP has initial structure. Furthermore, we consider a category L-CLS of L-valued closure spaces, obtaining its relation with L-valued Moore closure, and provide examples in relation to L-valued subgroups that produce Moore collection. Here we look at a category of L-valued closure groups, L-CLGRP proving that it is a topological category. Finally, we obtain a relationship between L-GRP and L-TransTOLGRP, the category of L-transitive tolerance groups besides adding some properties of L-valued closures of L-valued subgroups on L-valued topological groups.

Author Biographies

  • TMG Ahsanullah, King Saud University
    Department of Mathematics, Professor
  • Fawzi Al-Thukair, King Saud University
    Associate Pprofessor of Mathematics






Nonlinear Analysis

How to Cite

On the Aspects of Enriched Lattice-valued Topological Groups and Closure of Lattice-valued Subgroups. (2021). European Journal of Pure and Applied Mathematics, 14(3), 949-968. https://doi.org/10.29020/nybg.ejpam.v14i3.4021

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