Related papers: Existentially closed models and locally zero-dimen…

Classification, up to isomorphism, of algebras from a non-empty subset of the variety of $n$- dimensional algebras is presented. It is shown that these algebras have only trivial automorphism and if the basic field is algebraically closed…

We investigate a number of simple toy models to explore interesting relationships between dynamics and typicality. We start with an infinite model that has been proposed as an illustration of how non-ergodic dynamics can produce interesting…

Local properties of the fundamental group of a path-connected topological space can pose obstructions to the applicability of covering space theory. A generalized covering map is a generalization of the classical notion of covering map…

We consider varieties generated by finite closure algebras whose canonical relations have two levels, and whose restriction to a level is an "extremal" relation, i.e. the identity or the universal relation. The corresponding logics have…

We combine Homotopy Type Theory with axiomatic cohesion, expressing the latter internally with a version of "adjoint logic" in which the discretization and codiscretization modalities are characterized using a judgmental formalism of "crisp…

We present a class of mappings between models with topological mass mechanism and purely topological models in arbitrary dimensions. These mappings are established by directly mapping the fields of one model in terms of the fields of the…

We study the topology of a class of proper submodules and some of its distinguished subclasses and call them structure spaces. We give several criteria for the quasi-compactness of these structure spaces. We study $T_0$ and $T_1$ separation…

One considers geometry with the intransitive equaivalence relation. Such a geometry is a physical geometry, i.e. it is described completely by the world function, which is a half of the squared distance function. The physical geometry…

A generalization of topos theory is proposed giving an abstract realization of such categories as, say, the categories of manifolds and of Grothendieck schemes on the one hand, and permitting one, on the other hand, a view on…

We discuss here geometric structures of condensed matters by means of a fundamental topological method. Any geometric pattern can be universally represented by a decomposition space of a topological space consisting of the infinite product…

Preliminary evidence is presented that a long overlooked and critical element in the fundamental definition of a general theory of integration over curved Wess-Zumino superspace lies with the imposition of ``the Ethereal Conjecture'' which…

The existence and nature of singularities in locally spatially homogeneous solutions of the Einstein equations coupled to various phenomenological matter models is investigated. It is shown that, under certain reasonable assumptions on the…

Let k be an algebraically closed field of characteristic zero, F its algebraically closed extension, and G be the group of k-automorphisms of F endowed with a natural topology. One of the purposes of this paper is to show that any…

Manifolds all of whose geodesics are closed have been studied a lot, but there are only few examples known. The situation is different if one allows in addition for orbifold singularities. We show, nevertheless, that the abundance of new…

Earlier an arbitrary poset $P$ was proved to be isomorphic to the collection of subsets of a space $M$ with two closures which are closed in the first closure and open in the other. As a space $M$ for this representation an algebraic dual…

For a fixed ring, different classes of ring epimorphisms and localisation maps are compared. In fact, we provide sufficient conditions for a ring epimorphism to be a universal localisation. Furthermore, we consider recollements induced by…

Without leaving finite mathematics and using finite topological spaces only, we give a definition of homeomorphisms of finite abstract simplicial complexes or finite graphs. Besides exploring the definition in various contexts, we add some…

Global-type formalisms enable to describe the overall behaviour of distributed systems and at the same time to enforce safety properties for communications between system components. Our goal is that of amending a weakness of such…

We introduce the notion of a good map between topological spaces: a continuous map $f:X \to Y$ is *good* if for every non-empty irreducible locally closed subset $U \subseteq X$, there exists a non-empty open subset $W \subseteq Y$ such…

We develop the theory of topoi internal to an arbitrary $\infty$-topos $\mathcal B$. We provide several characterisations of these, including an internal analogue of Lurie's characterisation of $\infty$-topoi, but also a description in…