On the continuous action of enriched lattice-valued convergence groups: Some examples by T. M. G. Ahsanullah, Fawzi Al-Thukair and Jawaher Al-Mufarrij

Journal Article
Ahsanullah, T. M. G. . 2020
Publication Work Type
Original Research Article
Magazine \ Newspaper
Filomat
Issue Number
9
Volume Number
34
Pages
3045 to 3064
Conference Date
Publication Abstract

Abstract: Starting with a category SLCONVGRP, of stratified enriched cl-premonoid-valued convergence groups as introduced earlier, we present a category SLCONVTGRP, 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.

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