Related papers: Maps of metric spaces
This paper is about similarity between objects that can be represented as points in metric measure spaces. A metric measure space is a metric space that is also equipped with a measure. For example, a network with distances between its…
It is proved that the Gromov-Hausdorff metric on the space of compact metric spaces considered up to an isometry is strictly intrinsic, i.e., the corresponding metric space is geodesic. In other words, each two points of this space (each…
We give a brief survey of many of the high-lights of our present understanding of the young subject of quantum metric spaces, and of quantum Gromov-Hausdorff distance between them. We include examples.
Gromov introduced two distance functions, the box distance and the observable distance, on the space of isomorphism classes of metric measure spaces and developed the convergence theory of metric measure spaces. We investigate several…
We give a short introduction to the theory of modular metric spaces. This is a corrected version of the paper [1], which had some errors. We are grateful to V. V. Chistyakov for bringing these to our attention.
In this paper we study the geometry of graph spaces endowed with a special class of graph edit distances. The focus is on geometrical results useful for statistical pattern recognition. The main result is the Graph Representation Theorem.…
This is a detailed introductory survey of the cohomological dimension theory of compact metric spaces.
This is just a note for \cite[Chapter$3{1/2}_+$]{gromov}. Maybe this note is obvious for a reader who knows metric geometry. I wish that someone study further in this direction.
This report introduces and investigates a family of metrics on sets of pointed Kripke models. The metrics are generalizations of the Hamming distance applicable to countably infinite binary strings and, by extension, logical theories or…
In this paper, we study the geometry of non-Archimedean Gromov-Hausdorff metric. This is the first part of our series work, which we try to establish some facts about the counterpart of Gromov-Hausdorff metric in the non-Archimedean spaces.…
Graphs are interesting structures: extremely useful to depict real-life problems, extremely easy to understand given a sketch, extremely complicated to represent formally, extremely complicated to compare. Phylogeny is the study of the…
In spacetime physics, we frequently need to consider a set of all spaces (`universes') as a whole. In particular, the concept of `closeness' between spaces is essential. However, there has been no established mathematical theory so far…
Given strong local Dirichlet forms and $\mathbb{R}^N$-valued functions on a metrizable space, we introduce the concepts of geodesic distance and intrinsic distance on the basis of these objects. They are defined in a geometric and an…
Metric graphs are ubiquitous in science and engineering. For example, many data are drawn from hidden spaces that are graph-like, such as the cosmic web. A metric graph offers one of the simplest yet still meaningful ways to represent the…
We show that all the standard distances from metric geometry and functional analysis, such as Gromov-Hausdorff distance, Banach-Mazur distance, Kadets distance, Lipschitz distance, Net distance, and Hausdorff-Lipschitz distance have all the…
In this article, we introduce the concept of lexicographic metric space and, after discussing some basic properties of these metric spaces, such as completeness, boundedness, compactness and separability, we obtain a formula for the metric…
The purpose of this paper is twofold. On a technical side, we propose an extension of the Hausdorff distance from metric spaces to spaces equipped with asymmetric distance measures. Specifically, we focus on the family of Bregman…
We develop a matricial version of Rieffel's Gromov-Hausdorff distance for compact quantum metric spaces within the setting of operator systems and unital C*-algebras. Our approach yields a metric space of ``isometric'' unital complete order…
Can the spatial distance between two identical particles be explained in terms of the extent that one can be distinguished from the other? Is the geometry of space a macroscopic manifestation of an underlying microscopic statistical…
These informal notes briefly discuss some basic topics involving Lipschitz functions, connectedness, and Hausdorff content in particular.