Related papers: On Haar meager sets
We show that Haar measures of connected semisimple groups, embedded via a representation into a matrix space, have a homogeneous asymptotic limit when viewed from far away and appropriately rescaled. This is still true if the Haar measure…
The classification of high-dimensional data defined on graphs is particularly difficult when the graph geometry is unknown. We introduce a Haar scattering transform on graphs, which computes invariant signal descriptors. It is implemented…
A new definition of random sets is proposed. It is based on the distance in measurable space and uses negative definite kernels for continuation from initial space to that of random sets. This approach has no connection to Hausdorff…
A successful theme in the development of triangulated categories has been the study of compact objects. A weak dual notion called 0-cocompact objects was introduced in arXiv:1801.07995, motivated by the fact that sets of such objects…
We address the problem of computing a Minimal Dominating Set in highly dynamic distributed systems. We assume weak connectivity, i.e., the network may be disconnected at each time instant and topological changes are unpredictable. We make…
In these self-contained low prerequisite introductory notes we first present (in part 1) basic concepts of set theory and algebra without explicit category theory. We then present (in part 2) basic category theory involving a somewhat…
We introduce the notion of a graph derangement, which naturally interpolates between perfect matchings and Hamiltonian cycles. We give a necessary and sufficient condition for the existence of graph derangements on a locally finite graph.…
We define a motivic analogue of the Haar measure for groups of the form G(k((t))), where k is an algebraically closed field of characteristic zero, and G is a reductive algebraic group defined over k. A classical Haar measure on such groups…
We study a strengthening of the notion of a universally meager set and its dual counterpart that strengthens the notion of a universally null set. We say that a subset $A$ of a perfect Polish space $X$ is countably perfectly meager…
We explore an application of homological algebra to set theoretic objects by developing a cohomology theory for Hausdorff gaps. The cohomology theory is introduced with enough generality to be applicable to other questions in set theory.…
In this paper we introduce a new homology theory devoted to the study of families such as semi-algebraic or subanalytic families and in general to any family definable in an o-minimal structure (such as Denjoy-Carleman definable or $ln-exp$…
The notions of null-sets and nullity are present in all discourses of mathematics. They are based on the dual-pair of notions of "almost-every" and "almost none". A notion of nullity corresponds to a choice of subsets that one interprets as…
Recommender systems have become an essential instrument in a wide range of industries to personalize the user experience. A significant issue that has captured both researchers' and industry experts' attention is the cold start problem for…
H. Furstenberg introduced the notion of central sets in terms of topological dynamics and established the famous Central Sets Theorem. Later in [A new and stronger Central Sets Theorem, Fund. Math. 199 (2008), 155-175], D. De, N. Hindman,…
Molodtsov \cite{molodtsov-1999} proposed the concept of soft set theory in 1999, which can be used as a mathematical tool for dealing with problems that contain uncertainty. Sabir and Naz \cite{shabir-2013} defined notion of bipolar soft…
The cumulative hierarchy conception of set, which is based on the conception that sets are inductively generated from "former" sets, is generally considered a good way to create a set conception that seems safe from contradictions. This…
This document comprises Level Theory, parts 1-3. PART 1. The following bare-bones story introduces the idea of a cumulative hierarchy of pure sets: 'Sets are arranged in stages. Every set is found at some stage. At any stage S: for any sets…
Extending the well-studied concept of graphical regular representations to bipartite graphs, a Haar graphical representation (HGR) of a group $G$ is a bipartite graph whose automorphism group is isomorphic to $G$ and acts semiregularly with…
Let $(G,\cdot)$ be a Polish group. We say that a set $X \subset G$ is Haar null if there exists a universally measurable set $U \supset X$ and a Borel probability measure $\mu$ such that for every $g, h \in G$ we have $\mu(gUh)=0$. We call…
Hierarchical structures of motion exist across research fields, including computer vision, graphics, and robotics, where complex dynamics typically arise from coordinated interactions among simpler motion components. Existing methods to…