Lipschitz Maps on Trees
نویسنده
چکیده
We introduce and study a metric notion for trees and relate it to a conjecture of Shelah [10] about the existence of a finite basis for a class of linear orderings.
منابع مشابه
Lipschitz quotients from metric trees and from Banach spaces containing l1
A Lipschitz map f between the metric spaces X and Y is called a Lipschitz quotient map if there is a C > 0 (the smallest such C, the co-Lipschitz constant, is denoted coLip(f), while Lip(f) denotes the Lipschitz constant of f) so that for every x ∈ X and r > 0, fBX(x, r) ⊃ BY (f(x), r/C). Thus Lipschitz quotient maps are surjective maps which by definition have the property ensured by the open ...
متن کاملOn Gromov Hyperbolicity and a Characterization of Real Trees
Our argument relies on the well-known fact that Lipschitz maps from Euclidean space into metric spaces have metric derivatives almost everywhere, as proved by Kirchheim [Kir] and Korevaar-Schoen [KoSc] independently. We can combine the main result of [ChNi], a characterization of Gromov hyperbolicity via asymptotic cones [Dru], and Theorem 1.1 to obtain a partial generalization of Chatterji and...
متن کاملCharacterizations of Metric Trees and Gromov Hyperbolic Spaces
A. In this note we give new characterizations of metric trees and Gromov hyperbolic spaces and generalize recent results of Chatterji and Niblo. Our results have a purely metric character, however, their proofs involve two classical tools from analysis: Stokes’ formula in R2 and a Rademacher type differentiation theorem for Lipschitz maps. This analytic approach can be used to give chara...
متن کاملThe Space of Probabilistic 1-lipschitz Maps
We introduce and study a natural notion of probabilistic 1Lipschitz maps. We prove that the space of all probabilistic 1-Lipschitz maps defined on a probabilistic metric space G is also a probabilistic metric space. Moreover, when G is a group, then the space of all probabilistic 1-Lipschitz maps defined on G can be endowed with a monoid structure. Then, we caracterize the probabilistic invaria...
متن کاملApproximation of o-minimal maps satisfying a Lipschitz condition
Consider an o-minimal expansion of the real field. We show that definable Lipschitz continuous maps can be definably fine approximated by definable continuously differentiable Lipschitz maps whose Lipschitz constant is close to that of the original map.
متن کامل