Stratified LMN-convergence tower groups and their stratified LMN-uniform convergence tower structures

摘要

If Land Mare frames, and N is a quantale, then using stratification mappings between frames, we introduce a category of stratified LMN-convergence tower groups - a topological category. We then prove that every stratified LMN-limit tower group induces a stratified LMN-uniform convergence tower space. Also, we introduce a category of stratified LMN-Cauchy tower groups, and show that the category of strongly normal stratified LMN-limit tower groups, is isomorphic to the category of stratified LMN-Cauchy tower groups. We provide various examples in support of our theories so far developed herein the text. (C) 2017 Elsevier B.V. All rights reserved.