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Fuzzy Sets and Systems, 1998
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Kankana Chakrabarty +2 more
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Kankana Chakrabarty +2 more
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Order, 2011
A metric space (X, d) is called monotone if there is a linear order < on X and a constant c such that d(x, y) ⩽ c d(x, z) for all x < y < z in X. Topological properties of monotone metric spaces and their countable unions are investigated.
Ales Nekvinda, Ondrej Zindulka
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A metric space (X, d) is called monotone if there is a linear order < on X and a constant c such that d(x, y) ⩽ c d(x, z) for all x < y < z in X. Topological properties of monotone metric spaces and their countable unions are investigated.
Ales Nekvinda, Ondrej Zindulka
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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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Algebra universalis, 2012
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Kinematics in the metric space
Computers & Graphics, 2019Abstract This paper proposes a general method for driving kinematics by distances and more specifically for controlling kinematically articulated systems. Unlike traditional approaches, the problem is addressed in the metric space using distances belonging to points of the skeleton and to the environment.
Le Naour, Thibaut +2 more
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2020
The target of this paper is to induce a topology from a given $b_2$-metric and study the properties of the topology induced by this way. We first define the notion of $\varepsilon$-ball in $b_2$-metric spaces and consider the topology induced by a given $b_2$-metric via $\varepsilon$-balls.
GÜNER, Elif, AYGÜN, Halis
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The target of this paper is to induce a topology from a given $b_2$-metric and study the properties of the topology induced by this way. We first define the notion of $\varepsilon$-ball in $b_2$-metric spaces and consider the topology induced by a given $b_2$-metric via $\varepsilon$-balls.
GÜNER, Elif, AYGÜN, Halis
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Journal of Intelligent & Fuzzy Systems, 2018
The paper considers new classes of spaces of finite, bounded, measurable multisets with different metrics, pseudometrics, quasimetrics, symmetrics, and some properties of these metrics. We discuss the possibilities to apply new types of metrics for estimating proximity of objects with many numerical and/or verbal attributes.
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The paper considers new classes of spaces of finite, bounded, measurable multisets with different metrics, pseudometrics, quasimetrics, symmetrics, and some properties of these metrics. We discuss the possibilities to apply new types of metrics for estimating proximity of objects with many numerical and/or verbal attributes.
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2003
This is a presentation without proofs of the key facts about the topology of Probabilistic Metric spaces, Probabilistic Normed spaces and Probabilistic Inner Product spaces.
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This is a presentation without proofs of the key facts about the topology of Probabilistic Metric spaces, Probabilistic Normed spaces and Probabilistic Inner Product spaces.
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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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