Concepts inUltra-low-dimensional embeddings for doubling metrics
Embedding
In mathematics, an embedding (or imbedding) is one instance of some mathematical structure contained within another instance, such as a group that is a subgroup. When some object X is said to be embedded in another object Y, the embedding is given by some injective and structure-preserving map f : X ¿ Y. The precise meaning of "structure-preserving" depends on the kind of mathematical structure of which X and Y are instances.
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Joram Lindenstrauss
Joram Lindenstrauss (October 28, 1936 ¿ April 29, 2012) was an Israeli mathematician working in functional analysis. He was a professor of mathematics at the Einstein Institute of Mathematics, Hebrew University of Jerusalem, Israel.
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Riemannian geometry
Elliptic geometry is also sometimes called "Riemannian geometry".
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Uniform norm
In mathematical analysis, the uniform norm assigns to real- or complex-valued bounded functions f defined on a set S the non-negative number This norm is also called the supremum norm, the Chebyshev norm, or the infinity norm. The name "uniform norm" derives from the fact that a sequence of functions converges to f under the metric derived from the uniform norm if and only if converges to uniformly .
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Jean Bourgain
Jean Bourgain (born 28 February 1954) is a Belgian mathematician. He has been a faculty member at the University of Illinois, Urbana-Champaign and, from 1985 until 1995, professor at Institut des Hautes Études Scientifiques at Bures-sur-Yvette in France, and since 1994 at the Institute for Advanced Study in Princeton, New Jersey. He is currently an editor for the prestigious Annals of Mathematics. He received his Ph.D. from the Vrije Universiteit Brussel in 1977.
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Extreme point
In mathematics, an extreme point of a convex set S in a real vector space is a point in S which does not lie in any open line segment joining two points of S. Intuitively, an extreme point is a "vertex" of S. The Krein¿Milman theorem states that if S is convex and compact in a locally convex space, then S is the closed convex hull of its extreme points: In particular, such a set has extreme points. The Krein¿Milman theorem is stated for locally convex topological vector spaces.
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Metric space
In mathematics, a metric space is a set where a notion of distance 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 space. In fact, the notion of "metric" is a generalization of the Euclidean metric arising from the four long-known properties of the Euclidean distance.
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Euclidean space
In mathematics, Euclidean space is the Euclidean plane and three-dimensional space of Euclidean geometry, as well as the generalizations of these notions to higher dimensions. The term ¿Euclidean¿ distinguishes these spaces from the curved spaces of non-Euclidean geometry and Einstein's general theory of relativity, and is named for the Greek mathematician Euclid of Alexandria.
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