Results 11 to 20 of about 1,082,995 (200)
Homotopy Theory of Ultrametric Spaces [PDF]
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 ...
Mihara, Tomoki
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Topological Algebra and its Applications, 2023 In this article, we study the λ\lambda -commuting of bounded linear operators on ultrametric Banach spaces and the determinant spectrum of ultrametric matrices.
Ettayb Jawad
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Probability measure monad on the category of ultrametric spaces [PDF]
Applied General Topology, 2008 The set of all probability measures with compact support on an ultrametric space can be endowed with a natural ultrametric. We show that the functor of probability measures with finite supports (respectively compact supports) forms a monad in the ...
O.B. Hubal, M.M. Zarichnyi
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Characterizations of Urysohn universal ultrametric spaces [PDF]
Analysis and Geometry in Metric SpacesIn this article, using the existence of infinite equidistant subsets of closed balls, we first characterize the injectivity of ultrametric spaces for finite ultrametric spaces. This method also gives characterizations of the Urysohn universal ultrametric
Ishiki Yoshito
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Ramsey degrees of finite ultrametric spaces, ultrametric Urysohn spaces and dynamics of their isometry groups [PDF]
European Journal of Combinatorics, 2009 We study Ramsey-theoretic properties of several natural classes of finite ultrametric spaces, describe the corresponding Urysohn spaces and compute a dynamical invariant attached to their isometry groups.
Nguyen Van The, Lionel
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Functionals, functors and ultrametric spaces
Pracì Mìžnarodnogo Geometričnogo Centru, 2014 We consider different classes of functionals defined on the set of continuous functions on ultrametric spaces. Similarly as in the case of probability measures, idempotent measures, max-min measures and upper semicontinuous capacities we endow the sets ...
Лидия Базилевич +2 more
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Trees and ultrametric spaces: a categorical equivalence [PDF]
Advances in Mathematics, 2004 A well-known correspondence between infinite trees and ultrametric spaces exists, which takes into account the end space of the tree. The present paper deeply analyzes this correspondence in terms of categories, by introducing suitable categories that capture the geometry of trees at infinity and the micro-geometry of ultrametric spaces.
Hughes, Bruce, Bruce Hughes
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Morphological Semigroups and Scale-Spaces on Ultrametric Spaces [PDF]
, 2017 Ultrametric spaces are the natural mathematical structure to deal with data embedded into a hierarchical representation. This kind of representations is ubiquitous in morphological image processing, from pyramids of nested partitions to more abstract dendrograms from minimum spanning trees.
Jesús Angulo, Santiago Velasco-Forero
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On metric structure of ultrametric spaces [PDF]
Journal of Physics A: Mathematical and General, 2004 In our work we have reconsidered the old problem of diffusion at the boundary of ultrametric tree from a "number theoretic" point of view. Namely, we use the modular functions (in particular, the Dedekind eta-function) to construct the "continuous" analog of the Cayley tree isometrically embedded in the Poincare upper half-plane.
Vasilyev, Oleg, Nechaev, Sergei
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Isomorphism of Trees and Isometry of Ultrametric Spaces
Theory and Applications of Graphs, 2020 We study the conditions under which the isometry of spaces with metrics generated by weights given on the edges of finite trees is equivalent to the isomorphism of these trees.
Oleksiy Dovgoshey
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