Related papers: Dependence spaces II
We develope the framework of transitional conditional independence. For this we introduce transition probability spaces and transitional random variables. These constructions will generalize, strengthen and unify previous notions of…
This paper introduces a notion of integrality that is suitable for non-commutative varieties. It is compatible with the usual notion of integrality for schemes. The function field and generic point of a non-commutative integral space are…
We present a versatile construction allowing one to obtain pairs of integer sets with infinite symmetric difference, infinite intersection, and identical representation functions.
We study homogeneity aspects of metric spaces in which all triples of distinct points admit pairwise different distances; such spaces are called isosceles-free. In particular, we characterize all homogeneous isosceles-free spaces up to…
The aim of this paper is to study the class of spaces with the FNS property and $\pi-\FNS$ property. We shown that compact spaces with the FNS property for some base consisting of cozero-sets are openly generated spaces and spaces with the…
This course introduces the fruitful links between model theory and a combinatoric of sets given by independence relations. An independence relation on a set is a ternary relation between subsets. Chapter 1 should be considered as an…
We enrich the setting of strongly stable ideals (SSI): We introduce shift modules, a module category encompassing SSI's. The recently introduced duality on SSI's is given an effective conceptual and computational setting. We study strongly…
We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. In this second part we introduce the fundamental concepts of topological spaces, convergence, and continuity, as…
We prove that in Lipschitz-free spaces the strong diameter two property, the diameter two property, and the local diameter two property coincide with their corresponding attaining variants.
We give a necessary condition for inclusion relations between discrete Morrey spaces which can be seen as a complement of the results in \cite{GKS,HS2}. We also prove another inclusion property of discrete Morrey spaces which can be viewed…
This paper studies the existence of solutions and, in particular, the well-posedness of a class of boundary control systems. Our main result provides explicit and verifiable conditions on the system data that guarantee continuous dependence…
We give a characterisation of the separable Banach spaces with the Daugavet property which is applied to study the Daugavet property in the projective tensor product of an $L$-embedded space with another non-zero Banach space. The former…
We reconsider the immediate exchange model and define a more general class of models where mass is split, exchanged and merged. We relate the splitting process to the symmetric inclusion process via thermalization and from that obtain…
When describing elastic deformations of a body sometimes it is worth to take in account elastic spatial dispersion. If spatial dispersion is weak, as usually happens, then it can be reduced to dependence of thermodynamic potential on strain…
In spacetime physics, we frequently need to consider a set of all spaces (`universes') as a whole. In particular, the concept of `closeness' between spaces is essential. However, there has been no established mathematical theory so far…
We introduce and prove the consistency of a new set theoretic axiom we call the \emph{Invariant Ideal Axiom}. The axiom enables us to provide (consistently) a full topological classification of countable sequential groups, as well as fully…
In this article we further develop the theory of valuation independence and study its relation with classical notions in valuation theory such as immediate and defectless extensions. We use this general theory to settle two open questions…
The potential of Edge Computing technologies is yet to be exploited for multi-domain, multi-party data-driven systems. One aspect that needs to be tackled for the realization of envisioned open edge Ecosystems, is the secure and trusted…
In a separably connected space any two points are contained in a separable connected subset. We show a mechanism that takes a connected bounded metric space and produces a complete connected metric space whose separablewise components form…
We introduce an atomic formula intuitively saying that given variables are independent from given other variables if a third set of variables is kept constant. We contrast this with dependence logic. We show that our independence atom gives…