Characterization of transitivity in L-tolerance spaces by convergence and closure by Gunther Jaeger and T. M. G. Ahsanullah
We show that the category of quantale-valued tolerance spaces is isomorphic to a category of quantale-valued convergence spaces. We define suitable quantale-valued closure functions and use them to characterize transitivity axioms. Furthermore, transitivity is characterized by convergence and diagonal axioms. Quantale-valued tolerance relations compatible with group structures are also characterized by convergence and it is shown that they are transitive.
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…
In this paper, we present several characterizations on approach groups, and ultra-approach groups. In doing so, we first give necessary and sufficient conditions for an approach structure to be…