Related papers: Automatic continuity for vector spaces with linear…

We study topological properties of automorphisms of 4-dimensional torus generated by integer symplectic matrices. The main classifying element is the structure of the topology of a foliation generated by unstable leaves of the automorphism.…

In this paper we introduce a new technique to prove the existence of closed subspaces of maximal dimension inside sets of topological vector sequence spaces. The results we prove cover some sequence spaces not studied before in the context…

We prove that every 2-local automorphism of the unitary group or the general linear group on a complex infinite-dimensional separable Hilbert space is an automorphism. Thus these types of transformations are completely determined by their…

A "tensor space" is a vector space equipped with a finite collection of multi-linear forms. In previous work, we showed that (for each signature) there exists a universal homogeneous tensor space, which is unique up to isomorphism. Here we…

Let V be a variety of not necessarily associative algebras, and A an inverse limit of nilpotent algebras A_i\in V, such that some finitely generated subalgebra S \subseteq A is dense in A under the inverse limit of the discrete topologies…

In this paper, we examine the notion of topological stability and its relation to the shadowing properties in zero-dimensional spaces. Several counter-examples on the topological stability and the shadowing properties are given. Also, we…

We classify all group topologies coarser than the topology of stabilizers of finite sets in the case of automorphism groups of countable free-homogeneous structures, Urysohn space and Urysohn sphere, among other related results.

Topological Data Analysis has grown in popularity in recent years as a way to apply tools from algebraic topology to large data sets. One of the main tools in topological data analysis is persistent homology. This paper uses undergraduate…

We prove that every automorphism of the category of free Lie algebras is a semi-inner automorphism.

Considering evolutionary equations in the sense of Picard, we identify a certain topology for material laws rendering the solution operator continuous if considered as a mapping from the material laws into the set of bounded linear…

We present several naturally occurring classes of spectral spaces using commutative algebra on pointed monoids. For this purpose, our main tools are finite type closure operations and continuous valuations on monoids which we introduce in…

We show that, for each finite algebra A, either it has symmetric term operations of all arities or else some finite algebra in the variety generated by A has two automorphisms without a common fixed point. We also show this two-automorphism…

We propose a novel approach for preserving topological structures of the input space in latent representations of autoencoders. Using persistent homology, a technique from topological data analysis, we calculate topological signatures of…

We study the differentiability properties of the topological equivalence between a uniformly asymptotically stable linear nonautonomous system and a perturbed system with suitable nonlinearities. For this purpose, we construct a uniformly…

Let G be a locally compact group, and let U be its unitary representation on a Hilbert space H. Endow the space L(H) of linear bounded operators on H with weak operator topology. We prove that if U is a measurable map from G to L(H) then it…

Convergence spaces are a generalization of topological spaces. The category of convergence spaces is well-suited for Algebraic Topology, one of the reasons is the existence of exponential objects provided by continuous convergence. In this…

We prove automatic continuity theorems for "decomposable" or "local" linear transformations between certain natural subspaces of operator algebras. The transformations involved are not algebra homomorphisms but often are module…

Persistent homology is a popular tool in Topological Data Analysis. It provides numerical characteristics of data sets which reflect global geometric properties. In order to be useful in practice, for example for feature generation in…

In this article we show that there are homeomorphisms of plane continua whose conjugacy class is residual and have the shadowing property.

Let $S$ be a seminorm on an infinite-dimensional real or complex vector space $X$. Our purpose in this note is to study the continuity and discontinuity properties of $S$ with respect to certain norm-topologies on $X$.