Results 11 to 20 of about 7,273 (258)

THE HAUSDORFF METRIC AND CLASSIFICATIONS OF COMPACTA

Bulletin of the London Mathematical Society, 2006
In this paper we use the Hausdorff metric to prove that two compact metric spaces are homeomorphic if and only if their canonical complements are uniformly homeomorphic. So, we take one of the two steps needed to prove that the difference between the homotopical and topological classifications of compact connected ANRs depends only on the difference ...
Alonso Morón, Manuel, González Gómez , A.   +1 more
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Metric trees in the Gromov--Hausdorff space [PDF]

Commentationes Mathematicae Universitatis Carolinae, 2023
9 pages. This paper is strongly rerated to my papers arXiv:2110.01881 and arXiv:2111.08199.
Ishiki, Yoshito
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Gromov–Hausdorff convergence of metric pairs and metric tuples

Differential Geometry and its Applications
We study the Gromov-Hausdorff convergence of metric pairs and metric tuples and prove the equivalence of different natural definitions of this concept. We also prove embedding, completeness and compactness theorems in this setting. Finally, we get a relative version of Fukaya's theorem about quotient spaces under Gromov--Hausdorff equivariant ...
Ana Almaraz Gómez, Mauricio Che
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THE HAUSDORFF METRIC AND ITS EXTENSIONS

Demonstratio Mathematica, 2002
Let \((X,\rho)\) be a metric space, \(({\mathcal R},d)\) the space of all nonempty compact subsets of \(X\), endowed with the Hausdorff metric \(d\), and \(\mathcal F\) the family of all closed subsets of \(X\). For \(f:\mathbb{R}\to\mathbb{R}\) such that \(f(t)>0\), for all \(t\in [0,\infty)\), and \(\int_{[0,\infty)} f(t) dt< \infty\), one can define
Moshokoa, Seithuti P., Seithuti P. Moshokoa   +1 more
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Effective Hausdorff Dimension in General Metric Spaces [PDF]

Theory of Computing Systems, 2018
We introduce the concept of effective dimension for a wide class of metric spaces whose metric is not necessarily based on a measure. Effective dimension was defined by Lutz (Inf. Comput., 187(1), 49–79, 2003) for Cantor space and has also been extended to Euclidean space.
Elvira Mayordomo, Mayordomo, E.
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Metric Mean Dimension and Mean Hausdorff Dimension Varying the Metric

Qualitative Theory of Dynamical Systems
AbstractLet $$f:\mathbb {M}\rightarrow \mathbb {M}$$ f : M → M be a continuous map on a compact metric space $$\mathbb {M}$$ M equipped with a fixed metric d, and ...
Becker, Alex Jenaro, Baraviera, Alexandre, Scopel, Érick, Muentes Acevedo, Jeovanny De Jesús   +3 more
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Menger Convexity and Hausdorff Metric

, 2019
12 ...
Gupta, Ajit Kumar, Mukherjee, Saikat
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A Note on Equivalence of G-Cone Metric Spaces and G-Metric Spaces

Journal of New Theory, 2023
This paper contains the equivalence between tvs-G cone metric and G-metric using a scalarization function $\zeta_p$, defined over a locally convex Hausdorff topological vector space. This function ensures that most studies on the existence and uniqueness
Tarapada Bag, Abhishikta Das
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"Why Pompeiu-Hausdorff metric instead of Hausdorff metric?"

Creative Mathematics and Informatics, 2022
"The distance between two sets, commonly called Hausdorff metric, is a very important mathematical concept, with plenty of applications in almost all scientific research areas. We suggest in this paper an update of its name as Pompeiu-Hausdorff metric (distance).
VASILE BERINDE, MĂDĂLINA PĂCURAR
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Some Results in Hausdorff Neutrosophic Metric Spaces on Hutchinson-Barnsley Operator

Ratio Mathematica, 2022
The main purpose of this paper is to prove the Neutrosophic contraction properties of the Hutchinson-Barnsley operator on the Neutrosophic hyperspace with respect to the Hausdorff Neutrosophic metrics.
Vinchu Balan Shakila, M Jeyaraman
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