- infinite-dimensional sphere
- мат.бесконечномерная сфера
English-Russian scientific dictionary. 2008.
infinite-dimensional sphere
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Sphere packing — In mathematics, sphere packing problems are problems concerning arrangements of non overlapping identical spheres which fill a space. Usually the space involved is three dimensional Euclidean space. However, sphere packing problems can be… … Wikipedia
Contractibility of unit sphere in Hilbert space — In topology, it is a surprising fact that the unit sphere in (infinite dimensional) Hilbert space is a contractible space, sinceno finite dimensional spheres are contractible.This can be demonstrated in several different ways. Topological proof… … Wikipedia
n-sphere — 2 sphere wireframe as an orthogonal projection Just as a … Wikipedia
N-sphere — can project a sphere s surface to a plane, it can also project a 3 sphere s surface into 3 space. This image shows three coordinate directions projected to 3 space:parallels (red), meridians (blue) and hypermeridians (green).Due to the conformal… … Wikipedia
Riemann sphere — The Riemann sphere can be visualized as the complex number plane wrapped around a sphere (by some form of stereographic projection – details are given below). In mathematics, the Riemann sphere (or extended complex plane), named after the 19th… … Wikipedia
Fuzzy sphere — is one of the simplest and most canonical examples of non commutative geometry. Ordinarily, the functions defined on a sphere form a commuting algebra. A fuzzy sphere differs from an ordinary sphere because the algebra of functions on it is not… … Wikipedia
3-sphere — Stereographic projection of the hypersphere s parallels (red), meridians (blue) and hypermeridians (green). Because this projection is conformal, the curves intersect each other orthogonally (in the yellow points) as in 4D. All curves are circles … Wikipedia
Lie sphere geometry — is a geometrical theory of planar or spatial geometry in which the fundamental concept is the circle or sphere. It was introduced by Sophus Lie in the nineteenth century. [The definitive modern textbook on Lie sphere geometry is Harvnb|Cecil|1992 … Wikipedia
Exotic sphere — In differential topology, a mathematical discipline, an exotic sphere is a differentiable manifold M that is homeomorphic but not diffeomorphic to the standard Euclidean n sphere. That is, M is a sphere from the point of view of all its… … Wikipedia
Homology sphere — In algebraic topology, a homology sphere is an n manifold X having the homology groups of an n sphere, for some integer n ≥ 1. That is, we have: H 0( X ,Z) = Z = H n ( X ,Z)and : H i ( X ,Z) = {0} for all other i .Therefore X is a connected space … Wikipedia
Unit tangent bundle — In mathematics, the unit tangent bundle of a Finsler manifold ( M , || . ||), denoted by UT( M ) or simply UT M , is a fiber bundle over M given by the disjoint union:mathrm{UT} (M) := coprod {x in M} left{ v in mathrm{T} {x} (M) left| | v | {x} … Wikipedia
