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Ultrametric Preserving Functions and Weak Similarities of Ultrametric Spaces$$^*$$ [PDF]

open access: yesP-Adic Numbers, Ultrametric Analysis, and Applications, 2021
18 pages, 1 ...
Ruslan Shanin, Dovgoshey Oleksiy
exaly   +4 more sources

Ultrametric spaces and logic programming

open access: yesThe Journal of Logic Programming, 2000
Summary: We prove a very general multivalued fixed point theorem for ultrametric spaces which at the same time is a generalization of the multivalued fixed point theorem of Khamsi, Kreinovich and Misane for generalized metric spaces and our (singlevalued) fixed point theorem for ultrametric spaces.
Paulo Ribenboim, Sibylla Priess-Crampe
exaly   +2 more sources

Wavelets on ultrametric spaces

open access: yesApplied and Computational Harmonic Analysis, 2005
The authors consider ultrametric spaces with a metric \(| xy| \) satisfying the strong triangle inequality \(| ab| \leq\max(| ac| ,| cd| )\) for all \(c\). They construct measures in ultrametric spaces and introduce bases in quadratically integrable (complex valued) function spaces.
A Yu Khrennikov
exaly   +2 more sources
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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
openaire   +2 more sources

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.
openaire   +2 more sources

Homotopy Theory of Ultrametric Spaces

Higher Structures, 2021
This paper gives a new foundation of ultrametric spaces in terms of model categories, which was inspired by global rigid geometry with due regard to connections between Archimedean analysis and non-Archimedean one. These two branches of analysis are connected by perturbing the triangle inequality through deformation of symmetric monoidal structures on ...
openaire   +2 more sources

The immersion of ultrametric spaces into Hahn spaces

open access: yesJournal 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
exaly   +3 more sources

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 ...
openaire   +1 more source

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