Related papers: Probabilistic Metric Spaces as enriched categories

We observe that the category of topological space, uniform spaces, and simplicial sets are all, in a natural way, full subcategories of the same larger category, namely the simplicial category of filters; this is, moreover, implicit in the…

Ge and Lin (2015) proved the existence and the uniqueness of p-Cauchy completions of partial metric spaces under symmetric denseness. They asked if every (non-empty) partial metric space $X$ has a p-Cauchy completion $\bar{X}$ such that $X$…

The so-called weighted solid Cauchy transform, from inside the unit disc into the complement of its closure, is considered and their basic properties such as boundedness is studied for appropriate probability measures. The action the disc…

We revisit several results on exponential integrability in probability spaces and derive some new ones. In particular, we give a quantitative form of recent results by Cianchi-Musil and Pick in the framework of Moser-Trudinger-type…

This paper concerns an analytic and numerical analysis of a class of weighted singular Cauchy integrals with exponential weights $w:=\exp(-Q)$ with finite moments and with smooth external fields $Q:\mathbb R\to [0,\infty)$, with varying…

Using generalized enriched categories, in this paper we show that Rosick\'{y}'s proof of cartesian closedness of the exact completion of the category of topological spaces can be extended to a wide range of topological categories over…

Properties of categories enriched over the category of metric spaces are investigated and applied to a study of constructions known from that category and the category of Banach spaces. For every class of morphisms satisfying a mild…

In this paper we study some basic properties of strong {\lambda}- statistical convergence of sequences in probabilistic metric (PM) spaces. We also introduce and study the notion of strong {\lambda}-statistically Cauchyness. Further…

In this paper we present different ways to parametrize subsets of the space of valuations on $K[x]$ extending a given valuation on $K$. We discuss the methods using pseudo-Cauchy sequences and approximation types. The method presented here…

This is the first of a series of papers on enriched infinity categories, seeking to reduce enriched higher category theory to the higher algebra of presentable infinity categories, which is better understood and can be approached via…

For a small quantaloid $\mathcal{Q}$, a $\mathcal{Q}$-closure space is a small category enriched in $\mathcal{Q}$ equipped with a closure operator on its presheaf category. We investigate $\mathcal{Q}$-closure spaces systematically with…

After calculating the Dushnik-Miller dimension of Minkowski spaces to be countable infinity, we define a novel notion of dimension for ordered spaces recovering the correct manifold dimension and obtain a corresponding obstruction for the…

In this paper, we define probabilistic n-Banach spaces along with some concepts in this field and study convergence in these spaces by some lemmas and theorem.

We prove a fixpoint theorem for contractions on Cauchy-complete quantale-enriched categories. It holds for any quantale whose underlying lattice is continuous, and applies to contractions whose control function is sequentially…

This paper provides a comprehensive overview of some of the foundational properties of categories enriched over quantaloids, along with several new results. We demonstrate that the category whose objects are quantaloid-enriched categories…

Finite frames can be viewed as mass points distributed in $N$-dimensional Euclidean space. As such they form a subclass of a larger and rich class of probability measures that we call probabilistic frames. We derive the basic properties of…

Resolving an open question of J. A. Carillo and G. Toscani, M. Stawiska recently proved that certain metric spaces of probability measures equipped with Fourier-based metrics are complete. In this note, we extend such Fourier-based metrics…

For any countable $CW$-complex $K$ and a cardinal number $\tau\geq\omega$ we construct a completely metrizable space $X(K,\tau)$ of weight $\tau$ with the following properties: $\e X(K,\tau)\leq K$, $X(K,\tau)$ is an absolute extensor for…

The primary objective of the present paper is to develop the theory of quantization dimension of an invariant measure associated with an iterated function system consisting of finite number of contractive infinitesimal similitudes in a…

We give a new scale of completeness conditions for exponential systems in two types of functional spaces on subsets of the complex plane. The first is the Banach spaces of functions that are continuous on a compact and simultaneously…