Quantale-valued Cauchy tower spaces and completeness by Gunther Jaeger and T. M. G. Ahsanullah
Jaeger, Gunther . 2021
Generalizing the concept of a probabilistic cauchy space, we introduce quantale-valued Cauchy tower spaces. These spaces encompass quantale-valued metric spaces, quantale-valued uniform (convergence) tower spaces and quantale-valued convergence tower groups. For special choices of the quantale, classical and probabilistic metric spaces are covered and probabilistic and approach Cauchy spaces arise. We also study completeness and completion in this setting and establish a connection to the Cauchy completeness of a quantale-valued metric space.
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…