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We study the matricial field (MF) property for certain reduced crossed product C*-algebras and their traces. Using classification techniques and induced K-theoretic dynamics, we show that reduced crossed products of ASH-algebras of real…
In this survey, my aim has been to discuss the use of sequences and countable sets in general topology. In this way I have been led to consider five different classes of topological spaces: first countable spaces, sequential spaces, Frechet…
Following the success of the so-called algebraic approach to the study of decision constraint satisfaction problems (CSPs), exact optimization of valued CSPs, and most recently promise CSPs, we propose an algebraic framework for valued…
An important result in real algebraic geometry is the projection theorem: every projection of a semialgebraic set is again semialgebraic. This theorem and some of its conclusions lie at the basis of many other results, for example the…
We study the Borel subsets of the plane that can be made closed by refining the Polish topology on the real line. These sets are called potentially closed. We first compare Borel subsets of the plane using products of continuous functions.…
A classical result in additive combinatorics, which is a combination of Balog-Szemer\'edi-Gowers theorem and a variant of Freiman's theorem due to Ruzsa, says that if a subset $A$ of $\mathbb{F}_p^n$ contains at least $c |A|^3$ additive…
Let C be a separable unital C*-algebra, not isomorphic to the complex numbers, equipped with a faithful tracial state. Let A be a unital direct limit of one dimensional NCCW complexes, also equipped with a faithful tracial state. Suppose…
We study the constrained minimum energy problem with an external field relative to the $\alpha$-Riesz kernel $|x-y|^{\alpha-n}$ of order $\alpha\in(0,n)$ for a generalized condenser $\mathbf A=(A_i)_{i\in I}$ in $\mathbb R^n$, $n\geqslant…
Convex semilattices are algebras that are at the same time a convex algebra and a semilattice, together with a distributivity axiom. These algebras have attracted some attention in the last years as suitable algebras for probability and…
I provide simplified proofs for each of the following fundamental theorems regarding selection principles: 1. The Quasinormal Convergence Theorem, due to the author and Zdomskyy, asserting that a certain, important property of the space of…
This paper gives two different proofs to a structural theorem of decreasing minimization (lexicographic optimization) on integrally convex sets. The theorem states that the set of decreasingly minimal elements of an integrally convex set…
In this paper, we discuss some questions about compactness in MV-topological spaces. More precisely, we first present a Tychonoff theorem for such a class of fuzzy topological spaces and some consequence of this result, among which, for…
We show, under some natural conditions, that the set of abelian points on the non-anomalous subset of a closed irreducible subvariety $X$ intersected with the union of connected algebraic subgroups of codimension at least $\dim X$ in a…
A virtual Markov chain (VMC) is a sequence $\{X_N\}_{N=0}^{\infty}$ of Markov chains (MCs) coupled together on the same probability space such that $X_N$ has state space $\{0,1,\ldots, N\}$ and such that removing all instances of $N~+~1$…
We consider a generalization of the Cheeger problem in a bounded, open set $\Omega$ by replacing the perimeter functional with a Finsler-type surface energy and the volume with suitable powers of a weighted volume. We show that any…
In this article, we study the Lipschitz Geometry at infinity of complex analytic sets and we obtain results on algebraicity of analytic sets and on Bernstein's problem. Moser's Bernstein Theorem says that a minimal hypersurface which is a…
In this work we present an extension of Chubanov's algorithm to the case of homogeneous feasibility problems over a symmetric cone K. As in Chubanov's method for linear feasibility problems, the algorithm consists of a basic procedure and a…
We will study some modifications to the notion of an exact C*-algebra by replacing the minimal tensor product with the reduced free product. First we will demonstrate how the reduced free product of a short exact sequence of C*-algebras…
We characterize the topological non-cancellative cones that are expressible as projective limits of finite powers of $[0,\infty]$. These are also the cones of lower semicontinuous extended-valued traces on AF C*-algebras. Our main result…
We prove a new patchworking theorem for singular algebraic curves, which states the following. Given a complex toric threefold $Y$ which fibers over ${\mathbb C}$ with a reduced reducible zero fiber $Y_0$ and other fibers $Y_t$ smooth, and…