Related papers: A strong boundedness result for separable Rosentha…

We show that it is consistent relative to a weakly compact cardinal that strong homology is additive and compactly supported within the class of locally compact separable metric spaces. This complements work of Marde\v{s}i\'{c} and Prasolov…

Inspired by a classical theorem of topological dimension theory, we prove that every geodesic metric space of asymptotic dimension $n$ containing a bi-infinite geodesic can be coarsely separated by a subset $S$ of asymptotic dimension equal…

We introduce an ordinal index which characterizes weak compactness of operators between Banach spaces. We study when classes consisting of operators having bounded index form a closed ideal, the distinctness of the classes, and the…

We study the bounded cohomology of certain groups acting on the Cantor set. More specifically, we consider the full group of homeomorphisms of the Cantor set as well as Thompson's group $V$. We prove that both of these groups are boundedly…

Let CBV denote the Banach algebra of all continuous real-valued functions of bounded variation, defined in [0,1]. We show that the set of strongly singular functions in CBV is nonseparably spaceable. We also prove that certain families of…

We present a characterization of spaces of strictly decreasing functions on trees in terms of bisequentiality. This characterization answers Questions 6.1 and 6.2 of "A filter on a collection of finite sets and Eberlein compacta" by T.…

We prove that bounded conciseness is a closed property in the space of marked groups. As a consequence, we reformulate a conjecture of Fern\'andez-Alcober and Shumyatsky [7] about conciseness in the class of residually finite groups.

In the field of radial basis functions mathematicians have been endeavouring to find infinitely differentiable and compactly supported radial functions. This kind of functions are extremely important for some reasons. First, its…

Prompted by an example related to the tensor algebra, we introduce and investigate a stronger version of the notion of separable functor that we call heavily separable. We test this notion on several functors traditionally connected to the…

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…

We study definably complete locally o-minimal expansions of ordered groups in this paper. A definable continuous function defined on a closed, bounded and definable set behave like a continuous function on a compact set. We demonstrate…

For a wide class of unbounded integral Hankel operators on the positive half-line, we prove essential self-adjointness on the set of smooth compactly supported functions.

The goal of this paper is to show the following result: For every integer $n\geq 2$ there is a countable orderable group such that its space of orders is countable and has Cantor-Bendixson rank $n$. We show this by explicitly constructing a…

In this article we study for which Cantor sets there exists a gauge-function h, such that the h-Hausdorff-measure is positive and finite. We show that the collection of sets for which this is true is dense in the set of all compact subsets…

We prove bounds for the covering numbers of classes of convex functions and convex sets in Euclidean space. Previous results require the underlying convex functions or sets to be uniformly bounded. We relax this assumption and replace it…

We study strongly separately continuous real-valued function defined on the Banach spaces $\ell_p$. Determining sets for the class of strongly separately continuous functions on $\ell_p$ are characterized. We prove that for every $1\le…

We prove a generalization of the Jordan canonical form theorem for a class of bounded linear operators on complex separable Hilbert spaces.

Every endofunctor of the category of classes is proved to be set-based in the sense of Aczel and Mendler, therefore, it has a final coalgebra. Other basic properties of these endofunctors are proved, e.g. the existence of a free completely…

We describe a self-homeomorphism $R$ of the Cantor set $X$ and then show that its conjugacy class in the Polish group $H(X)$ of all homeomorphisms of $X$ forms a dense $G_\delta$ subset of $H(X)$. We also provide an example of a locally…

It is well known that a pair of compact sets in $\mathbb{R}^d$ ($d \in \mathbb{N}$) can be separated by small deformations if the sum of their upper box dimensions is less than $d$. In this paper, we demonstrate that this dimension…