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THE METRIC DIMENSION OF METRIC MANIFOLDS
Bulletin of the Australian Mathematical Society, 2015In this paper we determine the metric dimension of $n$-dimensional metric $(X,G)$-manifolds. This category includes all Euclidean, hyperbolic and spherical manifolds as special cases.
Saeid Maghsoudi, Majid Heydarpour
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The Metric Dimension of Metric Spaces
Computational Methods and Function Theory, 2013Let $$(X,d)$$ be a metric space. A subset $$A$$ of
Alan F. Beardon, Sheng Bau
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Chaos, Solitons & Fractals, 2002
Abstract We briefly discuss the nature of space, its metric and dimension in the spirit of El Naschie's Cantorian space-time.
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Abstract We briefly discuss the nature of space, its metric and dimension in the spirit of El Naschie's Cantorian space-time.
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Continuation of the metric dimension
Siberian Mathematical Journal, 1983The author introduces two ``relative'' dimension functions: given \(A\subset X\), he defines \((1)\quad X \dim(A)\leq n\) if every finite closed cover of X has a finite closed refinement \(\xi\) with the order of \(\xi\cap A\) being \(\leq n+1\); and \((2)\quad Xd(A)\leq n\) if for every system of \((n+1)\) disjoint closed sets \((B_ i,C_ i)\) in X ...
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2008
Subsets of \({\mathbb R}^n\) may have “intrinsic” dimensions that are much lower than \(n\). Consider, for example, two distinct vectors \(\mathbf {a},\mathbf {b}\in {\mathbb R}^n\) and the line \(L = \{\mathbf {a}+ t \mathbf {b}\,\mid \,t \in {\mathbb R}\}\).
Dan A. Simovici, Chabane Djeraba
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Subsets of \({\mathbb R}^n\) may have “intrinsic” dimensions that are much lower than \(n\). Consider, for example, two distinct vectors \(\mathbf {a},\mathbf {b}\in {\mathbb R}^n\) and the line \(L = \{\mathbf {a}+ t \mathbf {b}\,\mid \,t \in {\mathbb R}\}\).
Dan A. Simovici, Chabane Djeraba
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AXIOMATICS OF THE DIMENSION OF METRIC SPACES
Mathematics of the USSR-Sbornik, 1973In this paper we prove that there exists a unique function dim X which assigns to every finite-dimensional metric space X an integer dX such that the following axioms are satisfied. Axiom 1. dTn = n (Tn is an n-dimensional simplex). Axiom 2. if all Xi are closed in . Axiom 3. For every X there exists a finite open cover ?
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Occlusal Vertical Dimension: Best Evidence Consensus Statement
Journal of Prosthodontics, 2021Charles J Goodacre +2 more
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Various dimension reduction techniques for high dimensional data analysis: a review
Artificial Intelligence Review, 2021Xueqing Yao +2 more
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