On the Aspects of Enriched Lattice-valued Topological Groups and Closure of Lattice-valued Subgroups
| Autor: | Tmg Ahsanullah, Fawzi Al-Thukair |
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| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Numerical Analysis Pure mathematics Algebra and Number Theory Group (mathematics) Applied Mathematics Structure (category theory) Lattice (discrete subgroup) Theoretical Computer Science Topological category Closure (computer programming) Mathematics::Category Theory Convergence (routing) Geometry and Topology Topological group Categorical variable Mathematics |
| Zdroj: | European Journal of Pure and Applied Mathematics. 14:949-968 |
| ISSN: | 1307-5543 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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