Results 1 to 10 of about 26 (26)

Algebraic entropy of endomorphisms of M-sets

Topological Algebra and its Applications, 2021
The usual notion of algebraic entropy associates to every group (monoid) endomorphism a value estimating the chaos created by the self-map. In this paper, we study the extension of this notion to arbitrary sets endowed with monoid actions, providing ...
Zava Nicolò
doaj   +1 more source

A Simple Proof of Dvoretzky-Type Theorem for Hausdorff Dimension in Doubling Spaces

Analysis and Geometry in Metric Spaces, 2022
The ultrametric skeleton theorem [Mendel, Naor 2013] implies, among other things, the following nonlinear Dvoretzky-type theorem for Hausdorff dimension: For any 0 < β < α, any compact metric space X of Hausdorff dimension α contains a subset which is ...
Mendel Manor
doaj   +1 more source

On L1-Embeddability of Unions of L1-Embeddable Metric Spaces and of Twisted Unions of Hypercubes

Analysis and Geometry in Metric Spaces, 2022
We study properties of twisted unions of metric spaces introduced in [Johnson, Lindenstrauss, and Schechtman 1986], and in [Naor and Rabani 2017]. In particular, we prove that under certain natural mild assumptions twisted unions of L1-embeddable metric ...
Ostrovskii Mikhail I., Randrianantoanina Beata   +1 more
doaj   +1 more source

Hyperbolic Metric Spaces and Stochastic Embeddings

Forum of Mathematics, Sigma
Stochastic embeddings of finite metric spaces into graph-theoretic trees have proven to be a vital tool for constructing approximation algorithms in theoretical computer science.
Chris Gartland
doaj   +1 more source

Contractibility of boundaries of cocompact convex sets and embeddings of limit sets

Analysis and Geometry in Metric Spaces
We provide sufficient conditions as to when a boundary component of a cocompact convex set in a CAT(0){\rm{CAT}}\left(0)-space is contractible. We then use this to study when the limit set of a quasi-convex, codimension one subgroup of a negatively ...
Bregman Corey, Incerti-Medici Merlin
doaj   +1 more source

Uniform undistortion from barycentres, and applications to hierarchically hyperbolic groups

Analysis and Geometry in Metric Spaces
We show that infinite cyclic subgroups of groups acting uniformly properly on injective metric spaces are uniformly undistorted. In the special case of hierarchically hyperbolic groups, we use this to study translation lengths for actions on the ...
Abbott Carolyn, Hagen Mark, Petyt Harry, Zalloum Abdul   +3 more
doaj   +1 more source

Coarse entropy of metric spaces. [PDF]

Geom Dedic
Geller W, Misiurewicz M, Sawicki D.
europepmc   +1 more source

Transfinite asymptotic dimension and APD profiles

Topology and Its Applications, 2021
Takamitsu Yamauchi
exaly  

A complete metric space without non-trivial separable Lipschitz retracts

Journal of Functional Analysis, 2023
Petr Hajek, Andres Quilis
exaly  

Compact Hölder retractions and nearest point maps

Advances in Mathematics, 2023
Ruben Medina
exaly