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The Clone Space as a Metric Space
Acta Applicandae Mathematica, 1998Let \(O_k\), \(k\in\mathbb{N}\), be the set of all functions \(E^n_k\to E_k\) for some \(n\in\mathbb{N}\), where \(E_k=\{0,1,\dots,k-1\}\). Any subset \(C\) of \(O_k\) which contains all projections, i.e. functions defined by \(\text{pr}^n_i(x_1,x_2,\dots,x_n)=x_i\), \(1\leq i\leq n\), \(n\in\mathbb{N}\), and closed under superpositions is called a ...
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Journal of Mathematical Sciences, 2020
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Panzhensky, V. I. +2 more
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Panzhensky, V. I. +2 more
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Russian Mathematical Surveys, 2002
Summary: This survey discusses the problem of describing properties of the class of metric spaces in which the Uryson construction of a universal homogeneous metric space (for this class) can be carried out axiomatically. One of the main properties of this kind is the possibility of gluing together two metrics given on closed subsets and coinciding on ...
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Summary: This survey discusses the problem of describing properties of the class of metric spaces in which the Uryson construction of a universal homogeneous metric space (for this class) can be carried out axiomatically. One of the main properties of this kind is the possibility of gluing together two metrics given on closed subsets and coinciding on ...
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Theory of Probability & Its Applications, 1962
Let $\{ x_n ,n = 1,2, \cdots \}$ be a random sequence with values in a compact metric space X. Following Doss, we define the conditional mathematical expectation of $x_n $ with respect to the Borel field $\mathfrak{F}$ as the (random) set \[ M\left\{ {x_n \mid \mathfrak{F}} \right\} = \mathop \cup \limits_{y \in D} \left\{ {z:d\left( {z,y} \right ...
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Let $\{ x_n ,n = 1,2, \cdots \}$ be a random sequence with values in a compact metric space X. Following Doss, we define the conditional mathematical expectation of $x_n $ with respect to the Borel field $\mathfrak{F}$ as the (random) set \[ M\left\{ {x_n \mid \mathfrak{F}} \right\} = \mathop \cup \limits_{y \in D} \left\{ {z:d\left( {z,y} \right ...
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On metric spaces induced by fuzzy metric spaces
2016The authors introduce a family of extended pseudo-metrics for a class of fuzzy metric spaces. It enables to construct a metric on fuzzy metric spaces and the induced metric space shares many properties with the given fuzzy metric space. For example the same topology is generated and the spaces have the same completeness. The authors present some simple
Qiu, D., Dong, R., Li, H.
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Southeast Asian Bulletin of Mathematics, 2003
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American Journal of Mathematics, 1931
Eine Menge \( R \) von Elementen \( a, b, \ldots \) heißt (nach Menger) ein halbmetrischer Raum, wenn je 2 Elementen \( a, b \) ein Abstand \( a b=b a \geqq 0 \) zugeordnet ist, der nur dann verschwindet, wenn \( a=b \) ist. Die Elemente \( a, b, \ldots \) heißen Punkte. Gilt für je 3 Punkte \( a, b, c \) die Dreiecksungleichung \( a c+b c \geqq a b, \)
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Eine Menge \( R \) von Elementen \( a, b, \ldots \) heißt (nach Menger) ein halbmetrischer Raum, wenn je 2 Elementen \( a, b \) ein Abstand \( a b=b a \geqq 0 \) zugeordnet ist, der nur dann verschwindet, wenn \( a=b \) ist. Die Elemente \( a, b, \ldots \) heißen Punkte. Gilt für je 3 Punkte \( a, b, c \) die Dreiecksungleichung \( a c+b c \geqq a b, \)
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Pivot selection for metric-space indexing
International Journal of Machine Learning and Cybernetics, 2016Rui Mao +4 more
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Responsive materials architected in space and time
Nature Reviews Materials, 2022Xiaoxing Xia +2 more
exaly