Related papers: Bounded tiles in $\mathbb{Q}_p$ are compact open s…

To a given tiling a non commutative space and the corresponding C*-algebra are constructed. This includes the definition of a topology on the groupoid induced by translations of the tiling. The algebra is also the algebra of observables for…

We show that the space of all bounded derivations from the disc algebra into its dual can be identified with the Hardy space $H^1$; using this, we infer that all such derivations are compact. Also, given a fixed derivation $D$, we construct…

An open (resp., closed) subset A of a topological space (X, T ) is called C-open (resp., C-closed) set if cl(A) \ A (resp., A \ int(A)) is a countable set. This paper aims to present the concept of C-open and C-closed sets. We first…

We investigate the rotation sets of open billiards in $\mathbb{R}^N$ for the natural observable related to a starting point of a given billiard trajectory. We prove that the general rotation set is convex and the set of all convex…

We prove that the centre of the category of smooth mod $p$ representations with fixed central character of a split semisimple $p$-adic group is a local ring.

We prove that a compact quantum group with faithful Haar state which has a faithful action on a compact space must be a Kac algebra, with bounded antipode and the square of the antipode being identity. The main tool in proving this is the…

In this paper, we give a characterization of compact sets in $L^p$-spaces on metric measure spaces, which is a generalization of the Kolmogorov-Riesz theorem. Using the criterion, we investigate the topological type of the space consisting…

The aim of this paper is to study the dimensions and standard part maps between the field of $p$-adic numbers ${{\mathbb Q}_p}$ and its elementary extension $K$ in the language of rings $L_r$. We show that for any $K$-definable set…

The periodic tiling conjecture asserts that if a region $\Sigma\subset \mathbb R^d$ tiles $\mathbb R^d$ by translations then it admits at least one fully periodic tiling. This conjecture is known to hold in $\mathbb R$, and recently it was…

In this paper we describe the blocks of the partition algebra over a field of positive characteristic.

In a recent paper \cite{T} the fact that a class of locally compact metric spaces $X$, among which are Euclidean spaces, are not homemorphic to their punctured version $X\men\{p\}$, was given an interesting new proof which does not use…

In this paper we define and study signed deficient topological measures and signed topological measures (which generalize signed measures) on locally compact spaces. We prove that a signed deficient topological measure is $\tau$-smooth on…

In this article, gentle algebras are realised as tiling algebras, which are associated to partial triangulations of unpunctured surfaces with marked points on the boundary. This notion of tiling algebras generalise the notion of Jacobian…

We prove a compactness criterion for asymptotic $L_p$ spaces over arbitrary measure spaces. Total boundedness is characterized by almost equiboundedness together with total boundedness in $L_p$ of all truncations. This gives a…

We prove that if f is a self-map of an algebraic variety over a field K, then under certain conditions on X, f and K the set of possible periods of K-valued periodic points of f is finite.

We show that any quantum family of maps from a non commutative space to a compact quantum metric space has a canonical quantum semi metric structure.

Below, by space we mean a separable metrizable zero-dimensional space. It is studied when the space can be embedded in a Cantor set while maintaining the algebraic structure. Main results of the work: every space is an open retract of a…

Let $p$ be a prime number. In this article we present a theorem, suggested by Peter Scholze, which states that the absolute Galois group of $\mathbf{Q}_p$ is the \'etale fundamental group of a certain object $Z$ which is defined over an…

We study self-similar attractors in the space $\mathbb{R}^d$, i.e., self-similar compact sets defined by several affine operators with the same linear part. The special case of attractors when the matrix $M$ of the linear part of affine…

Subsets of the set of $g$-tuples of matrices that are closed with respect to direct sums and compact in the free topology are characterized. They are, in a dilation theoretic sense, contained in the hull of a single point.