- Hausdorff manifold
- Математика: хаусдорфово многообразие
Универсальный англо-русский словарь. Академик.ру. 2011.
Hausdorff manifold
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Non-Hausdorff manifold — In mathematics, it is a usual axiom of a manifold to be a Hausdorff space, and this is assumed throughout geometry and topology: manifold means (second countable) Hausdorff manifold . In general topology, this axiom is relaxed, and one studies… … Wikipedia
Manifold — For other uses, see Manifold (disambiguation). The sphere (surface of a ball) is a two dimensional manifold since it can be represented by a collection of two dimensional maps. In mathematics (specifically in differential geometry and topology),… … Wikipedia
Hausdorff space — In topology and related branches of mathematics, a Hausdorff space, separated space or T2 space is a topological space in which distinct points have disjoint neighbourhoods. Of the many separation axioms that can be imposed on a topological space … Wikipedia
Topological manifold — In mathematics, a topological manifold is a Hausdorff topological space which looks locally like Euclidean space in a sense defined below. Topological manifolds form an important class of topological spaces with applications throughout… … Wikipedia
Gromov–Hausdorff convergence — Gromov–Hausdorff convergence, named after Mikhail Gromov and Felix Hausdorff, is a notion for convergence of metric spaces which is a generalization of Hausdorff convergence. Gromov–Hausdorff distanceGromov–Hausdorff distance measures how far two … Wikipedia
Locally Hausdorff space — In mathematics, in the field of topology, a topological space is said to be locally Hausdorff if every point has an open neighbourhood that is Hausdorff under the subspace topology.Here are some facts:* Every Hausdorff space is locally Hausdorff … Wikipedia
Differentiable manifold — A nondifferentiable atlas of charts for the globe. The results of calculus may not be compatible between charts if the atlas is not differentiable. In the middle chart the Tropic of Cancer is a smooth curve, whereas in the first it has a sharp… … Wikipedia
Riemannian manifold — In Riemannian geometry, a Riemannian manifold ( M , g ) (with Riemannian metric g ) is a real differentiable manifold M in which each tangent space is equipped with an inner product g in a manner which varies smoothly from point to point. The… … Wikipedia
Hilbert manifold — In mathematics, a Hilbert manifold is a manifold modeled on Hilbert spaces. Thus it is a separable Hausdorff space in which each point has a neighbourhood homeomorphic to an infinite dimensional Hilbert space. The concept of a Hilbert manifold… … Wikipedia
Collapsing manifold — For the concept in homotopy, see collapse (topology). In Riemannian geometry, a collapsing or collapsed manifold is an n dimensional manifold M that admits a sequence of Riemannian metrics gn, such that as n goes to infinity the manifold is close … Wikipedia
Sub-Riemannian manifold — In mathematics, a sub Riemannian manifold is a certain type of generalization of a Riemannian manifold. Roughly speaking, to measure distances in a sub Riemannian manifold,you are allowed to go only along curves tangent to so called horizontal… … Wikipedia
