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Bad Wadge-like reducibilities on the Baire space

Luca Motto Ros (2014)

Fundamenta Mathematicae

We consider various collections of functions from the Baire space $^{ω} ω$ into itself naturally arising in (effective) descriptive set theory and general topology, including computable (equivalently, recursive) functions, contraction mappings, and functions which are nonexpansive or Lipschitz with respect to suitable complete ultrametrics on $^{ω} ω$ (compatible with its standard topology). We analyze the degree-structures induced by such sets of functions when used as reducibility notions between subsets of...

Banach's Mappings And Some Generalizations

M. R. Tasković (1973)

Publications de l'Institut Mathématique

Bend sets, $N$ -sequences, and mappings.

Charatonik, Janusz J., Illanes, Alejandro (2004)

International Journal of Mathematics and Mathematical Sciences

Bi-Lipschitz Bijections of Z

Itai Benjamini, Alexander Shamov (2015)

Analysis and Geometry in Metric Spaces

It is shown that every bi-Lipschitz bijection from Z to itself is at a bounded L1 distance from either the identity or the reflection.We then comment on the group-theoretic properties of the action of bi-Lipschitz bijections.

Bilipschitz embeddings of metric spaces into euclidean spaces.

Stephen Semmes (1999)

Publicacions Matemàtiques

When does a metric space admit a bilipschitz embedding into some finite-dimensional Euclidean space? There does not seem to be a simple answer to this question. Results of Assouad [A1], [A2], [A3] do provide a simple answer if one permits some small ("snowflake") deformations of the metric, but unfortunately these deformations immediately disrupt some basic aspects of geometry and analysis, like rectifiability, differentiability, and curves of finite length. Here we discuss a (somewhat technical)...

Bochner's formula for harmonic maps from Finsler manifolds

Jintang Li (2008)

Colloquium Mathematicae

Let ϕ :(M,F)→ (N,h) be a harmonic map from a Finsler manifold to any Riemannian manifold. We establish Bochner's formula for the energy density of ϕ and maximum principle on Finsler manifolds, from which we deduce some properties of harmonic maps ϕ.