Related papers: Infinitary Noetherian Constructions I. Infinite Wo…

We define E-theory for separable C*-algebras over second countable topological spaces and establish its basic properties. This includes an approximation theorem that relates the E-theory over a general space to the E-theories over finite…

We construct natural symbolic representations of intrinsically ergodic, but not necessarily expansive, principal algebraic actions of countably infinite amenable groups and use these representations to find explicit generating partitions…

Various kinds of infinitary operations satisfying forms of associativity have been considered in the literature by various authors, including A. Tarski, C. Karp, J. H. Conway, D. Krob, N. Bedon, and C. Rispal. Applications include the…

We perform the computations necessary to establish a multiplicity one statement for the irreducible representations of a finite spin group which in turn yields the classification of irreducible representations of finite spin groups. (The…

We consider the dimensions of finite type of representations of a partially ordered set, i.e. such that there is only finitely many isomorphism classes of representations of this dimension. We give a criterion for a dimension to be of…

In this paper we study the number of finite topologies on an $n$-element set subject to various restrictions.

These expository notes are dedicated to the study of the topology of configuration spaces of manifolds. We give detailed computations of many invariants, including the fundamental group of the configuration spaces of $\mathbb{R}^2$, the…

We analyse properties of hypertoric manifolds of infinite topological type, including their topology and complex structures. We show that our manifolds have the homotopy type of an infinite union of compact toric varieties. We also discuss…

We construct classifying spaces for discrete and compact Lie groups, with the property that they are topological groups and complete metric spaces in a natural way. We sketch a program in view of extending these constructions.

In this article we study injective representations of infinite quivers. We classify the indecomposable injective representations of trees and then describe Gorenstein injective and projective representations of barren trees.

An intersection of sets $A = \bigcap_{i \in I}B_i$ is irredundant if no $B_i$ can be omitted from this intersection. We develop a topological approach to irredundance by introducing a notion of a spectral representation, a spectral space…

In this paper we study a relationship between systems of $n$ subspaces and representations of $*$-algebras generated by projections. We prove that irreducible nonequivalent $*$-representations of $*$-algebras $\mathcal P_{4,com}$ generate…

We prove the following. Let $R$ be a Noetherian ring, $B$ a finitely generated $R$-algebra, and $A$ a pure $R$-subalgebra of $B$. Then $A$ is finitely generated over $R$.

Using von Neumann algebras, we extend the theory of quantum computation on a graph to a theory of computation on an arbitrary topological space.

There are many examples of the fact that dimension and codimension behave somewhat counterintuitively. In EGA it is stated that a topological space is equidimensional, equicodimensional and catenary if and only if every maximal chain of…

The intended model of the homotopy type theories used in Univalent Foundations is the infinity-category of homotopy types, also known as infinity-groupoids. The problem of higher structures is that of constructing the homotopy types needed…

It is shown that vielbeins and connections of any (super)space are naturally described in terms of nonlinear realizations of infinite - dimensional diffeomorphism groups of the corresponding (super)space. The method of construction of…

We consider and characterize classes of finite and countably categorical structures and their theories preserved under $E$-operators and $P$-operators. We describe $e$-spectra and families of finite cardinalities for structures belonging to…

We distinguish a class of irreducible finite representations of conformal Lie (super)algebras. These representations (called universally defined) are the simplest ones from the computational point of view: a universally defined…

We study equations over relational structures that approximate groups and semigroups. For such structures we proved the criteria, when a direct power of such algebraic structures is equationally Noetherian.