We present a Coq formalization of ultrametric spaces and of ultrametric-enriched categories, up to and including the construction of solutions to recursive domain equations in ultrametric-enriched categories. We then show how to apply this semantic setup for giving semantics to a programming language with higher-order store. Specifically, we define a step counting operational semantics for a fu...

The question posed in the title of this article has been raised by Hans Frauenfelder over 20 years ago [1]. When studying the ligand-rebinding kinetics of myoglobin, Frauenfelder discovered that below the room temperature, at which the protein dynamics limit the rebinding rate, the reaction kinetics obeys a power law or a stretched exponent [2]. In order to explain this fact, he supposed that t...

Prompted by a recent question of G. Hjorth [12] as to whether a bounded Urysohn space is indivisible, that is to say has the property that any partition into finitely many pieces has one piece which contains an isometric copy of the space, we answer this question and more generally investigate partitions of countable metric spaces. We show that an indivisible metric space must be totally Cantor...

There is a well-known correspondence between infinite trees and ultrametric spaces that comes from considering the end space of the tree. The correspondence is interpreted here as an equivalence between two categories, one of which encodes the geometry of trees at infinity and the other encodes the micro-geometry of complete ultrametric spaces. r 2003 Elsevier Inc. All rights reserved. MSC: pri...

Finite sets S of points in a Euclidean space the mutual distances of which satisfy the ultrametric inequality (A;B) maxf (A;C); (C;B)g for all points in S are investigated and geometrically characterized. Inspired by results on ultrametric matrices and previous results on simplices, connections with so-called centered metric trees as well as with strongly isosceles right simplices are found. AM...

In this paper we prove that there is an immersion of every ultrametric space X into a Hahn space associated to X. It is not assumed that the set of distances of X is totally ordered.

in this paper, vector ultrametric spaces are introduced and a fixed point theorem is given forcorrespondences. our main result generalizes a known theorem in ordinary ultrametric spaces.

In this paper, vector ultrametric spaces are introduced and a fixed point theorem is given for correspondences. Our main result generalizes a known theorem in ordinary ultrametric spaces.

The ultrametric skeleton theorem [Mendel, Naor 2013] implies, among other things, the following nonlinear Dvoretzky-type for Hausdorff dimension: For any $0<\beta<\alpha$, compact metric space $X$ of dimension $\alpha$ contains a subset which is biLipschitz equivalent to an and has at least $\beta$. In this note we present simple proof in doubling spaces using Bartal's Ramsey decompositions [Ba...