Related papers: Probabilistic Metric Spaces as enriched categories
This is a complete classification of the complex forms of quaternionic symmetric spaces
In this paper we study properties of complete sets and of completions of sets in Banach spaces. We consider the family of completions of a given set and its size; we also study in detail the relationships concerning diameters, radii, and…
We give an answer to the following question: for which metric in an abstract lattice the completion as a metric space coincides with the completion as a lattice. We obtain the answer for inductive limits of lattices which are complete in…
The invertibility hypothesis for a monoidal model category S asks that localizing an S-enriched category with respect to an equivalence results in an weakly equivalent enriched category. This is the most technical among the axioms for S to…
We describe all metric spaces that have sufficently many affine functions. As an application we obtain a metric characterization of linear-convex subsets of Banach spaces.
We develop an analog to the ends of a metric space for the category of coarse metric spaces and show that it is equivalent to a previously defined coarse invariant.
In this paper, we investigate Kondratiev spaces on domains of polyhedral type. In particular, we will be concerned with necessary and sufficient conditions for continuous and compact embeddings, and in addition we shall deal with pointwise…
In this paper, we give some interesting identities of poly-Cauchy numbers and polynomials arising from umbral calculus.
We survey some old and new results concerning the classification of complete metric spaces up to isometry, a theme initiated by Gromov, Vershik and others. All theorems concerning separable spaces appeared in various papers in the last…
The Giry monad on the category of measurable spaces sends a space to a space of all probability measures on it. There is also a finitely additive Giry monad in which probability measures are replaced by finitely additive probability…
We investigate an enriched-categorical approach to a field of discrete mathematics. The main result is a duality theorem between a class of enriched categories (called $\overline{\mathbb{Z}}$- or $\overline{\mathbb{R}}$-categories) and that…
In a recent paper, two multi-representations for the measurable sets in a computable measure space have been introduced, which prove to be topologically complete w.r.t. certain topological properties. In this contribution, we show them…
In this work we study the space complexity of computable real numbers represented by fast convergent Cauchy sequences. We show the existence of families of trascendental numbers which are logspace computable, as opposed to algebraic…
Parabolic integro-differential model Cauchy problem is considered in the scale of Lp -spaces of functions whose regularity is defined by a scalable Levy measure. Existence and uniqueness of a solution is proved by deriving apriori…
In this paper we examine two basic topological properties of partial metric spaces, namely compactness and completeness. Our main result claims that in these spaces compactness is equivalent to sequential compactness. We also show that…
Real-enriched categories are categories with real numbers as enrichment. Precisely, a real-enriched category is a category enriched over the commutative and unital quantale composed of the unit interval and a continuous t-norm. These notes…
We introduced a new continued fraction expansions in our previous paper. For these expansions, we show formulae of probability about incomplete quotients. Furthermore, we prove the existence of invariant measures with respect to the…
The probabilistic type spaces in the sense of Harsanyi [Management Sci. 14 (1967/68) 159--182, 320--334, 486--502] are the prevalent models used to describe interactive uncertainty. In this paper we examine the existence of a universal type…
Finite dimensional subspaces spanned by exponential functions in the space of square integrable functions on a finite interval of the real line are considered. Their limiting positions are studied and described in terms of expo-polynomials.
We consider weighted banach spaces of holomorphic functions on the upper half plane that are determined by $ \|f\|=\sup_{y>0,-\infty<x<\infty}p(y)|f(x+iy)|<\infty $ for a very large class of weight functions p. We completely solve the…