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19 relations: American Mathematical Society, Carathéodory's theorem (convex hull), Cardinality, Choquet theory, Compact space, Convex hull, Convex set, Discrete geometry, Eduard Helly, Finite intersection property, German Mathematical Society, Heinrich Guggenheimer, Helly family, Intersection (set theory), Krein–Milman theorem, Mathematical induction, Mathematische Annalen, Radon's theorem, Shapley–Folkman lemma.
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.
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Carathéodory's theorem (convex hull)
In convex geometry, Carathéodory's theorem states that if a point x of Rd lies in the convex hull of a set P, then x can be written as the convex combination of at most d + 1 points in P. Namely, there is a subset ′ of P consisting of d + 1 or fewer points such that x lies in the convex hull of ′.
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Cardinality
In mathematics, the cardinality of a set is a measure of the "number of elements of the set".
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Choquet theory
In mathematics, Choquet theory, named after Gustave Choquet, is an area of functional analysis and convex analysis concerned with measures which have support on the extreme points of a convex set C. Roughly speaking, every vector of C should appear as a weighted average of extreme points, a concept made more precise by generalizing the notion of weighted average from a convex combination to an integral taken over the set E of extreme points.
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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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Convex hull
In mathematics, the convex hull or convex envelope or convex closure of a set X of points in the Euclidean plane or in a Euclidean space (or, more generally, in an affine space over the reals) is the smallest convex set that contains X. For instance, when X is a bounded subset of the plane, the convex hull may be visualized as the shape enclosed by a rubber band stretched around X., p. 3.
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Convex set
In convex geometry, a convex set is a subset of an affine space that is closed under convex combinations.
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Discrete geometry
Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects.
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Eduard Helly
Eduard Helly (June 1, 1884, Vienna – 1943, Chicago) was a mathematician after whom Helly's theorem, Helly families, Helly's selection theorem, Helly metric, and the Helly–Bray theorem were named.
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Finite intersection property
In general topology, a branch of mathematics, a collection A of subsets of a set X is said to have the finite intersection property (FIP) if the intersection over any finite subcollection of A is nonempty.
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German Mathematical Society
The German Mathematical Society (Deutsche Mathematiker-Vereinigung – DMV) is the main professional society of German mathematicians.
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Heinrich Guggenheimer
Heinrich Walter Guggenheimer (born 21 July 1924) is a German-born American mathematician who has contributed to knowledge in differential geometry, topology, algebraic geometry, and convexity.
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Helly family
In combinatorics, a Helly family of order k is a family of sets such that any minimal subfamily with an empty intersection has k or fewer sets in it.
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Intersection (set theory)
In mathematics, the intersection A ∩ B of two sets A and B is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements.
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Krein–Milman theorem
In the mathematical theory of functional analysis, the Krein–Milman theorem is a proposition about convex sets in topological vector spaces.
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Mathematical induction
Mathematical induction is a mathematical proof technique.
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Mathematische Annalen
Mathematische Annalen (abbreviated as Math. Ann. or, formerly, Math. Annal.) is a German mathematical research journal founded in 1868 by Alfred Clebsch and Carl Neumann.
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Radon's theorem
In geometry, Radon's theorem on convex sets, published by Johann Radon in 1921, states that any set of d + 2 points in Rd can be partitioned into two disjoint sets whose convex hulls intersect.
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Shapley–Folkman lemma
The Shapley–Folkman lemma is a result in convex geometry with applications in mathematical economics that describes the Minkowski addition of sets in a vector space.
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