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metric convexity

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  • Metric space — In mathematics, a metric space is a set where a notion of distance (called a metric) between elements of the set is defined. The metric space which most closely corresponds to our intuitive understanding of space is the 3 dimensional Euclidean… …   Wikipedia

  • Convex metric space — An illustration of a 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. Formally, consider a… …   Wikipedia

  • Modulus and characteristic of convexity — In mathematics, the modulus and characteristic of convexity are measures of how convex the unit ball in a Banach space is. In some sense, the modulus of convexity has the same relationship to the ε δ definition of uniform convexity as the modulus …   Wikipedia

  • Glossary of Riemannian and metric geometry — This is a glossary of some terms used in Riemannian geometry and metric geometry mdash; it doesn t cover the terminology of differential topology. The following articles may also be useful. These either contain specialised vocabulary or provide… …   Wikipedia

  • Geodesic convexity — In mathematics mdash; specifically, in Riemannian geometry mdash; geodesic convexity is a natural generalization of convexity for sets and functions to Riemannian manifolds. It is common to drop the prefix geodesic and refer simply to convexity… …   Wikipedia

  • Differential geometry of surfaces — Carl Friedrich Gauss in 1828 In mathematics, the differential geometry of surfaces deals with smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces have been extensively studied from various perspectives:… …   Wikipedia

  • Locally convex topological vector space — In functional analysis and related areas of mathematics, locally convex topological vector spaces or locally convex spaces are examples of topological vector spaces (TVS) which generalize normed spaces. They can be defined as topological vector… …   Wikipedia

  • Lp space — In mathematics, the Lp spaces are function spaces defined using a natural generalization of the p norm for finite dimensional vector spaces. They are sometimes called Lebesgue spaces, named after Henri Lebesgue (Dunford Schwartz 1958, III.3),… …   Wikipedia

  • Convex set — A convex set …   Wikipedia

  • Median graph — The median of three vertices in a median graph In mathematics, and more specifically graph theory, a median graph is an undirected graph in which any three vertices a, b, and c have a unique median: a vertex m(a,b,c) that belongs to shortest… …   Wikipedia

  • Orthogonal convex hull — The orthogonal convex hull of a point set In Euclidean geometry, a set is defined to be orthogonally convex if, for every line L that is parallel to one of the axes of the Cartesian coordinate system, the intersection of K with L is empty, a… …   Wikipedia

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