On the continuous action of enriched lattice-valued convergence groups: Some examples by T. M. G. Ahsanullah, Fawzi Al-Thukair and Jawaher Al-Mufarrij
Ahsanullah, T. M. G. . 2020
Abstract: Starting with a category SL- CONVGRP, of stratified enriched cl-premonoid-valued convergence groups as introduced earlier, we present a category SL- CONVTGRP, of stratified enriched cl-premonoid-valued convergence transformation groups, the idea behind this category is crept in the notion of convergence transformation group - a generalization of topological transformation group. In this respect, we are able to provide natural examples in support to our endeavor; these examples, however, stem from the action of convergence approach groups on convergence approach spaces, and the action of probabilistic convergence groups under triangular norm on probabilistic convergence spaces. Based on the category of enriched lattice-valued convergence spaces, a Cartesian closed category that enjoys lattice-valued convergence structure on function space, we look into among others, the lattice-valued convergence structures on the group of homeomorphisms of enriched lattice-valued convergence spaces, generalizing a concept of convergence transformation groups on convergence spaces, obtaining a characterization.
Generalizing the notion of probabilistic convergence ring, where the underlying lattice is a specific quantale, we consider more general quantale to introduce the notions of quantale…
Considering a value quantale, we introduce a category of quantale-valued convergence transformation groups on quantale-valued convergence spaces.
In this article, we focus on discussing some subcategories of the category of probabilistic convergence groups, PConvGrp. In so doing, we introduce a category of probabilistic…