Manifold

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Edits to this page may be lost. Please contribute instead at manifold/rewrite.

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:This page is about a higher mathematics topic. For other meanings of the word manifold, see manifold (disambiguation).

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In mathematics, a manifold is a topological space that looks locally like the Euclidean space Rn, and the Euclidean space indeed provides the simplest example of a manifold. The surface of a sphere such as the Earth provides a more complicated example. A general manifold can be obtained by bending and gluing together flat regions.

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Manifolds are used in mathematics to describe geometrical objects and they provide the natural arena to study differentiability. In physics, manifolds serve as the phase space in classical mechanics and four-dimensional pseudo-Riemannian manifolds are used to model the spacetime in general relativity. They also occur as configuration spaces. The torus is the configuration space of the double pendulum.

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Topological space: Topological spaces are structures that allow one to formalize concepts such as convergence, connectedness and continuity. They appear in virtually every branch of modern mathematics and are a central unifying notion. The branch of mathematics that studies topological spaces in their own right is cal...

Locally: In mathematics, something is said to occur locally in the category of topological spaces if it occurs on "small enough" open sets....

Euclidean space: In mathematics, Euclidean space is a generalization of the 2- and 3-dimensional spaces studied by Euclid. The generalization applies Euclid's concept of distance, and the related concepts of length and angle, to a coordinate system in any number of dimensions. It is the "standard" example of a finit...

Manifold related Images and Photos (experimental)

Calabi-Yau Manifold Glass Sculpture