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Lipschitz-Free Spaces Over Ultrametric Spaces [PDF]

Mediterranean Journal of Mathematics, 2015
The only change in the latest version is the second author's grant information. Question 1 from the previous version has been answered - see Remark 15 for the solution. Preprint was accepted in Mediterr.
Marek Cúth, Michal Doucha
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On the universal ultrametric space

Ukrainian Mathematical Journal, 1994
Summary: An ultrametric space in which any separable ultrametric space is isometrically imbedded is constructed. We show how, by using this universal space, any separable ultrametric space can be imbedded into \(l_1\), \(l_2\) and \(c_0\).
Igor Vestfrid
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Dynamics on Ultrametric Spaces

Physical Review Letters, 1985
We present an exact solution to the problem of a random walk on an ultrametric space with arbitrary transition probabilities. The solution provides a description of fluctuation dynamics of systems with many degenerate states separated by a hierarchy of energy barriers.
, Ogielski, , Stein
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Generalized ultrametric spaces II

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 1996
The authors study ultrametric spaces \((X, d, \Gamma)\), where \(X\) is a nonempty set, \(\Gamma\) a partially ordered set with smallest element \(0\), and \(d: X\times X \rightarrow\Gamma\) a (surjective) ultrametric distance function (i.e., \(d(x,y)=0\) if and only if \(x=y\), \(d(x,y)=d(y,x)\), if \(d(x,y) \leq \gamma\) and \(d(y,z) \leq \gamma ...
Priess-Crampe, S., Ribenboim, P.
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The immersion of ultrametric spaces into Hahn spaces

Journal of Algebra, 2010
The immersion of an ultrametric space with totally ordered set of distances into a spherically complete ultrametric space was established independently by \textit{S. Priess-Crampe} and \textit{P. Ribenboim} [Abh. Math. Semin. Univ. Hamb. 67, 19--31 (1997; Zbl 0887.54029)] and by \textit{E. Schörner} [Result. Math. 29, No.~3--4, 361--370 (1996; Zbl 0866.
Paulo Ribenboim
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On a universal ultrametric space

Topology and Its Applications, 2000
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lemin, Alex J., Lemin, Vladimir A.
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On Immediate Extensions of Ultrametric Spaces

Results in Mathematics, 1996
Let \(\Gamma\cup\{0\}\) be a totally ordered set with 0 as the first element, \(X\) be a nonempty set. A mapping \(d:X\times X\to \Gamma\cup \{0\}\) is called ultrametric distance if for all \(x,y,z\) from \(X\) the following axioms hold: (1) \(d(x,y)=0 \iff x=y\), (2) \(d(x,y)=d(y,x)\), (3) \(d(x,y)\leq \max(d(x,z), d(z,y))\).
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Subordination on ultrametric spaces

Journal of Physics A: Mathematical and General, 1987
Using the formalism of continuous-time random walks (CTRW) the authors discuss particle diffusion on ultrametric spaces (UMS). For broad waiting time distributions psi (t) approximately t- alpha -1 the temporal ( alpha ) and the energetic ( gamma ) parameters combine multiplicatively (subordinate): i.e.
G Kohler, A Blumen
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A Hyperbolic Filling for Ultrametric Spaces

Computational Methods and Function Theory, 2014
Let \((X,d)\) and \((Y,d^{\prime})\) be Gromov 0-hyperbolic spaces, whose boundaries at infinity \(\partial X\) and \(\partial Y\) are equipped with the canonical visual metrics. The author first shows that an isometry at infinity \(f: X \to Y\) has a canonical extension to a map \(\partial f: \partial X \to \partial Y\) and that the extension is a ...
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Optimal clustering method in ultrametric spaces

2011 IEEE Symposium on Computers and Communications (ISCC), 2011
Resume We propose in this paper a novel clustering algorithm in ultrametric spaces. It has a computational cost of O(n). This method is based on the ultratriangle inequality property. Using the order of ultrametric space we demonstrate that we can deduce the proximities between all data in this space with just a few informations.
Said Fouchal, Murat Ahat, Ivan Lavallée
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