26 relations: Angle, Arc length, Closed set, Compact space, Comparison of topologies, Complete metric space, Continuous function, Convex metric space, Euclidean space, Finsler manifold, Geodesic, Great-circle distance, Hopf–Rinow theorem, Infimum and supremum, Karl Menger, Locally compact space, Mathematics, Metric space, Metric Structures for Riemannian and Non-Riemannian Spaces, Radian, Riemannian circle, Riemannian manifold, Sphere, Sub-Riemannian manifold, Topological space, Unit circle.
Angle
In plane geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
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Arc length
Determining the length of an irregular arc segment is also called rectification of a curve.
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Closed set
In geometry, topology, and related branches of mathematics, a closed set is a set whose complement is an open set.
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Compact space
In mathematics, and more specifically in general topology, compactness is a property that generalizes the notion of a subset of Euclidean space being closed (that is, containing all its limit points) and bounded (that is, having all its points lie within some fixed distance of each other).
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Comparison of topologies
In topology and related areas of mathematics, the set of all possible topologies on a given set forms a partially ordered set.
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Complete metric space
In mathematical analysis, a metric space M is called complete (or a Cauchy space) if every Cauchy sequence of points in M has a limit that is also in M or, alternatively, if every Cauchy sequence in M converges in M. Intuitively, a space is complete if there are no "points missing" from it (inside or at the boundary).
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Continuous function
In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.
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Convex metric space
In mathematics, convex metric spaces are, intuitively, metric spaces with the property any "segment" joining two points in that space has other points in it besides the endpoints.
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Euclidean space
In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.
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Finsler manifold
In mathematics, particularly differential geometry, a Finsler manifold is a differentiable manifold where a (possibly asymmetric) Minkowski norm is provided on each tangent space, allowing to define the length of any smooth curve as Finsler manifolds are more general than Riemannian manifolds since the tangent norms need not be induced by inner products.
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Geodesic
In differential geometry, a geodesic is a generalization of the notion of a "straight line" to "curved spaces".
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Great-circle distance
The great-circle distance or orthodromic distance is the shortest distance between two points on the surface of a sphere, measured along the surface of the sphere (as opposed to a straight line through the sphere's interior).
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Hopf–Rinow theorem
Hopf–Rinow theorem is a set of statements about the geodesic completeness of Riemannian manifolds.
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Infimum and supremum
In mathematics, the infimum (abbreviated inf; plural infima) of a subset S of a partially ordered set T is the greatest element in T that is less than or equal to all elements of S, if such an element exists.
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Karl Menger
Karl Menger (January 13, 1902 – October 5, 1985) was an Austrian-American mathematician.
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Locally compact space
In topology and related branches of mathematics, a topological space is called locally compact if, roughly speaking, each small portion of the space looks like a small portion of a compact space.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Metric space
In mathematics, a metric space is a set for which distances between all members of the set are defined.
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Metric Structures for Riemannian and Non-Riemannian Spaces
Metric Structures for Riemannian and Non-Riemannian Spaces is a book in geometry by Mikhail Gromov.
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Radian
The radian (SI symbol rad) is the SI unit for measuring angles, and is the standard unit of angular measure used in many areas of mathematics.
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Riemannian circle
In metric space theory and Riemannian geometry, the Riemannian circle is a great circle equipped with its great-circle distance.
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Riemannian manifold
In differential geometry, a (smooth) Riemannian manifold or (smooth) Riemannian space (M,g) is a real, smooth manifold M equipped with an inner product g_p on the tangent space T_pM at each point p that varies smoothly from point to point in the sense that if X and Y are differentiable vector fields on M, then p \mapsto g_p(X(p),Y(p)) is a smooth function.
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Sphere
A sphere (from Greek σφαῖρα — sphaira, "globe, ball") is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball (viz., analogous to the circular objects in two dimensions, where a "circle" circumscribes its "disk").
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Sub-Riemannian manifold
In mathematics, a sub-Riemannian manifold is a certain type of generalization of a Riemannian manifold.
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Topological space
In topology and related branches of mathematics, a topological space may be defined as a set of points, along with a set of neighbourhoods for each point, satisfying a set of axioms relating points and neighbourhoods.
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Unit circle
In mathematics, a unit circle is a circle with a radius of one.
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Redirects here:
Length metric space, Length space, Length-metric space, Metric convexity.
References
[1] https://en.wikipedia.org/wiki/Intrinsic_metric