Open AccessOn the Aspects of Enriched Lattice-valued Topological Groups and Closure of Lattice-valued Subgroups
Author(s) -
T. M. G. Ahsanullah,
Fawzi Al-Thukair
Publication year - 2021
Publication title -
european journal of pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.245
H-Index - 5
ISSN - 1307-5543
DOI - 10.29020/nybg.ejpam.v14i3.4021
Subject(s) - mathematics , closure (psychology) , topological group , categorical variable , lattice (music) , topological space , group (periodic table) , transitive closure , group action , topology (electrical circuits) , combinatorics , discrete mathematics , statistics , physics , chemistry , organic chemistry , economics , acoustics , market economy
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.