On the Aspects of Enriched Lattice-valued Topological Groups and Closure of Lattice-valued Subgroups
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.
Upon acceptance of an article by the journal, the author(s) accept(s) the transfer of copyright of the article to European Journal of Pure and Applied Mathematics.Â
European Journal of Pure and Applied Mathematics will be Copyrihgt Holder.
If necessary, authors are responsible for obtaining permissions to reprint previously published figures, tables, and other material.