Publications

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,...
We introduce categories of probabilistic uniform groups, PUGrp, and probabilistic uniform convergence groups, PUConvGrp; and show that there is an isomorphism between the category PUGrp and a subcategory of PUConvGrp. Considering an existing...
We introduce the categories of quantale-valued approach uniform spaces and quantale-valued uniform gauge spaces, and prove that they are topological categories. We first show that the category of quantale-valued uniform gauge spaces is a reflective...
The motive behind this article is to generalize the concept of approach groups. In so doing, we introduce various categories, specifically, the categories of quantale-valued convergence groups, quantale-valued approach groups, quantale-valued gauge...
We introduce a notion of a probabilistic convergence transformation group, and present various natural examples including quotient probabilistic convergence transformation group. In doing so, we construct a probabilistic convergence structure on the...
We identify two categories of quantale-valued convergence tower spaces that are isomorphic to the categories of quantale-valued metric spaces and quantale-valued partial metric spaces, respectively. As an application we state a quantale-valued...
Considering a complete Heyting algebra $\mathbb{H}$, we introduce a notion of stratified $\mathbb{H}$-convergence semigroup. We develop some basic facts on the subject, besides obtaining conditions under which a stratified $\mathbb{H}$-convergence...
If L and M are 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...
We define probabilistic convergence groups based on Tardiff's neighborhood systems for probabilistic metric spaces and develop the basic theory. We study, as natural examples, probabilistic metric groups and probabilistic normed groups as well as...
We propose here two types of probabilistic convergence groups under triangular norms; present some basic facts, and give some characterizations for both the cases. We look at the possible link from categorical point of view between each of the...
Considering a frame $L$, we introduce the notions of stratified $L$-semi-topological neighborhood group, stratified $L$-quasi-topological neighborhood group, and stratified $L$-quasi-bi-topological neighborhood group. In so doing, we look at the...
We develop a theory of probabilistic uniform convergence spaces based on Tardiff"s neighborhood systems for probabilistic metric spaces. We show that the resulting category is topological and Cartesian closed. A subcategory is idenified that is...
We discuss the compatibilities between approach limit structures and group structures; present some basic facts, provide several natural examples, and include some characterization theorems. Introducing the notions of approach pre-Cauchy group and...
We introduce probabilistic limit groups under a t-norm and study their basic properties. We show that for the classes of strict t-norms, all categories of probabilistic limit groups under such t-norms are isomorphic. The same is true for nilpotent t...
In this paper, we focus on enriched cl-premonoid-valued topological groups, and their so-called change-of-basis lattice. In so doing, we take L as an enrichedcl-premonoid and present a category SL-NTopGrp, of stratified enriched cl-premonoid-valued...
Considering a category SL-GConv, of stratified enriched cl-premonoid-valued generalized convergence spaces, we present thecategory SL-GConvGrp, of stratified L-generalized convergence groups, and some of its subcategories. We present two natural...