Related papers: Proximal and Descriptive Topological Rings: Struct…
We introduce the notion of a Tits arrangement on a convex open cone as a special case of (infinite) simplicial arrangements. Such an object carries a simplicial structure similar to the geometric representation of Coxeter groups. The…
Recently there has been a lot of research and progress in profinite groups. We survey some of the new results and discuss open problems. A central theme is decompositions of finite groups into bounded products of subsets of various kinds…
The kth finite subset space of a topological space X is the space exp_k X of non-empty finite subsets of X of size at most k, topologised as a quotient of X^k. The construction is a homotopy functor and may be regarded as a union of…
We study the set of localizations of an integral domain from a topological point of view, showing that it is always a spectral space and characterizing when it is a proconstructible subspace of the space of all overrings. We then study the…
We study monitorable sets from a topological standpoint. In particular, we use descriptive set theory to describe the complexity of the family of monitorable sets in a countable space $X$. When $X$ is second countable, we observe that the…
In this study, Devaney's chaos conditions are revisited within the framework of descriptive proximity. The concepts of descriptive transitivity, the density of descriptive periodic objects, and descriptive sensitivity are defined. The most…
Let G be a compact Lie group. By work of Chataur and Menichi, the homology of the space of free loops in the classifying space of G is known to be the value on the circle in a homological conformal field theory. This means in particular…
We study the topology of metric spaces which are definable in o-minimal expansions of ordered fields. We show that a definable metric space either contains an infinite definable discrete set or is definably homeomorphic to a definable set…
In this note, we compare and contrast various selective divergence properties such as the properties of being discretely selective and selectively highly divergent. We identify and incorporate a class of subsemigroups of the semigroup of…
We consider the Tate cohomology of the circle group acting on the topological Hochschild homology of schemes. We show that in the case of a scheme smooth and proper over a finite field, this cohomology theory naturally gives rise to the…
The subject of topological defects has become a very attractive field of study given its apparent relevance to as diverse systems as the early universe and condensed matter. As usually envisaged the topology of the manifold M of the minima…
This is a survey on the local structure about a fixed point of discrete finite-dimensional holomorphic dynamical systems, discussing in particular the existence of local topological conjugacies to normal forms, and the structure of local…
A visceral structure on M is given by a definable base for a uniform topology on its universe in which all basic open sets are infinite and any infinite definable subset X of M has non-empty interior. This context includes o-minimal ordered…
We investigate active particles that exhibit long-range interactions only restricted by a field of view, which is characterized by an angle $\beta$. We show that constraining attractive interactions to a field of view leads to the emergence…
This paper explores the concept of topological transitivity in nonautonomous dynamical systems, which are defined as sequences of continuous maps from a compact metric space to itself. It investigates various conditions (including…
Constant structure closed semantic systems are the systems each element of which receives its definition through the correspondent unchangeable set of other elements of the system. Discrete time means here that the definitions of the…
Let M be a manifold, and G a Lie group which satisfies the unique extension property. An (M,G) manifold N is a manifold endowed with an atlas (U_i,f_i) where f_i is a diffeomorphism between U_i and an open set of M such that the coordinates…
The purpose of this paper is to continue studying the properties of $\gamma$-regular open sets introduced and explored in [6]. The concept of $\gamma$-closed spaces have also been defined and discussed.
We investigate the role of the proximality relation for tiling dynamical systems. Under two hypotheses, namely that the minimal rank is finite and the set of fiber distal points has full measure we show that the following conditions are…
In the preprint arXiv:2511.07900 we proved that there exists a localizing ring $A_M$ for $A$ an associative ring with unit, and $M=\oplus_{i=1}^rM_i$ a direct sum of $r\geq 1$ simple right $A$-modules. For a homomorphism of associative…