Related papers: On separable nets in constructive topological spac…

We build on work of Elek and Zucker and develop a topological analogue of the theory of weak containment. We show that definitions in terms of local patterns, containment in ultra(co)products, and continuous model theory are all equivalent,…

The article is devoted to a structure of topological spaces related with topological quasigroups. Regular and complete spaces over topological quasigroups are studied. Separations and embeddings are also investigated for them. Their…

The group of piecewise projective homeomorphisms of the line provides straightforward counter-examples to the so-called von Neumann conjecture. The examples are so simple that many additional properties can be established.

Given a positively graded commutative coherent ring A which is finitely generated as an A_0-algebra, a bijection between the tensor Serre subcategories of qgr A and the set of all subsets Y\subseteq Proj A of the form…

We introduce a reducibility on classes of structures, essentially a uniform enumeration reducibility. This reducibility is inspired by the Friedman-Stanley paper on using Borel reductions to compare classes of countable structures. This…

Multinets are certain configurations of lines and points with multiplicities in the complex projective plane $\mathbb{P}^2$. They appear in the study of resonance and characteristic varieties of complex hyperplane arrangement complements…

We study groups of homeomorphic bijections on spaces that are finite unions of compact connected linearly ordered subsets. We prove that all such groups when endowed with the topology of point-wise convergence are topological groups. }

We investigate if an existing notion of weak sequential convergence in a Hadamard space can be induced by a topology. We provide an answer on what we call weakly proper Hadamard spaces. A notion of dual space is proposed and it is shown…

We develop a theory of rewriting for structured cospans in order to extend compositional methods for modeling open networks. First, we introduce a category whose objects are structured cospans, and establish conditions under which it is…

We consider finite systems of contractive homeomorphisms of a complete metric space, which are non-redundant on every level. In general this separation condition is weaker than the strong open set condition and is not equivalent to the weak…

In this paper, we present a number of examples of k-nets, which are special configurations of lines and points in the projective plane. Such a configuration can be regarded as the union of k completely reducible elements of a pencil of…

Given an idempotent complete additive category, we show the there is an explicitly constructed topological space such that the lattice of exact substructures is anti-isomorphic to the lattice of closed subsets. In the special case that the…

We introduce a novel technique for checking reachability in Petri nets that relies on a recently introduced compositional algebra of nets. We prove that the technique is correct, and discuss our implementation. We report promising…

In this paper, we go into the study of the 2-category SSS_\Sigma of \Sigma-constructible stacks. The notions of constructible stack was introduced by D. Treumann. It is a natural generalization of constructible sheaf. D. Treumann has also…

We prove that the well-known (strong) fully-concurrent bisimilarity and the novel i-causal-net bisimilarity, which is a sligtlhy coarser variant of causal-net bisimilarity, are decidable for finite bounded Petri nets. The proofs are based…

For the importance of differentiation theorems in metric spaces (starting with Pansu Rademacher type theorem in Carnot groups) and relations with rigidity of embeddings see the section 1.2 in Cheeger and Kleiner paper arXiv:math/0611954 and…

Consider a local chain Differential Graded algebra, such as the singular chain complex of a pathwise connected topological group. In two previous papers, a number of homological results were proved for such an algebra: An Amplitude…

We determine when a quasi-isometry between discrete spaces is at bounded distance from a bilipschitz map. From this we prove a geometric version of the Von Neumann conjecture on amenability. We also get some examples in geometric groups…

Networked structures arise in a wide array of different contexts such as technological and transportation infrastructures, social phenomena, and biological systems. These highly interconnected systems have recently been the focus of a great…

We formalise a general concept of distributed systems as sequential components interacting asynchronously. We define a corresponding class of Petri nets, called LSGA nets, and precisely characterise those system specifications which can be…