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metric space

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(mathematics) Any space whose elements are points, and between any two of which a non-negative real number can be defined as the distance between the points; an example is Euclidean space

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The metric space formed in this way from a polyhedron is called its development.
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Isomorphisms between metric spaces are called isometries.
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A metric space is called complete if all Cauchy sequences converge.
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Every Euclidean space is also a complete metric space.
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Similarly, in a metric space, positively separated sets are sets separated by a nonzero distance.
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Every metric space is also a topological space.
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A topological space is called metrizable, if it underlies a metric space.
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Every normed space is both a linear topological space and a metric space.
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The real line forms a metric space, with the distance function given by absolute difference: d(x, y) = | x − y | .
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Alexandrov's original proof does not lead to an algorithm for constructing the polyhedron (for instance by giving coordinates for its vertices) realizing the given metric space.
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The polyhedron representing the given metric space may be degenerate: it may form a doubly-covered two-dimensional convex polygon (a dihedron) rather than a fully three-dimensional polyhedron.
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Another result of Pogorelov on the geodesic metric spaces derived from convex polyhedra is a version of the theorem of the three geodesics: every convex polyhedron has at least three simple closed quasigeodesics.
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It implies that convex polyhedra with distinct shapes from each other also have distinct metric spaces of surface distances, and it characterizes the metric spaces that come from the surface distances on polyhedra.
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Analysis may be distinguished from geometry; however, it can be applied to any space of mathematical objects that has a definition of nearness (a topological space) or specific distances between objects (a metric space).
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The surface of any convex polyhedron in Euclidean space forms a metric space, in which the distance between two points is measured by the length of the shortest path from one point to the other along the surface.
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It states that if a metric space (X,d) is geodesic, homeomorphic to a sphere, and locally Euclidean except for a finite number of cone points of positive angular defect summing to 4π, then there exists a convex polyhedron whose development is (X,d).
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The development of any polyhedron can be described concretely by a collection of two-dimensional polygons together with instructions for gluing them together along their edges to form a metric space, and the conditions of Alexandrov's theorem for spaces described in this way are easily checked.
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Metric expansion of space: the universe is expanding, and the far parts of it are moving away from us faster than the speed of light.
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The Room Insights Dashboard gives you metrics to analyze how your organization uses space.
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Moreover, all geometric notions immanent to a Euclidean space can be characterized in terms of its metric.
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This is a differential manifold with a Finsler metric, that is, a Banach norm defined on each tangent space.
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In conjunction with the world-lines of freely falling particles, the light-cones can be used to reconstruct the space–time's semi-Riemannian metric, at least up to a positive scalar factor.
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The term "projective geometry" is used sometimes to indicate the generalised underlying abstract geometry, and sometimes to indicate a particular geometry of wide interest, such as the metric geometry of flat space which we analyse through the use of homogeneous coordinates, and in which Euclidean geometry may be embedded (hence its name, Extended Euclidean plane).
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Once the Anomaly detection model has been defined, Analysis applies a Bayesian state space-time series model to the training data to forecast the value of the metric displayed in the time series.
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In very elementary terms, anti-de Sitter space is a mathematical model of spacetime in which the notion of distance between points (the metric) is different from the notion of distance in ordinary Euclidean geometry.
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