Manifold
In mathematics, a manifold of dimension n is a topological space that near each point resembles n-dimensional Euclidean space. More precisely, each point of an n-dimensional manifold has a neighbourhood that is homeomorphic to the Euclidean space of dimension n. Lines and circles, but not figure eights, are one-dimensional manifolds. Two-dimensional manifolds are also called surfaces. Examples include the plane, the sphere, and the torus, which can all be realized in three dimensions, but also the Klein bottle and real projective plane which cannot.
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Famous quotes containing the word manifold:
“There is then creative reading as well as creative writing. When the mind is braced by labor and invention, the page of whatever book we read becomes luminous with manifold allusion. Every sentence is doubly significant, and the sense of our author is as broad as the world.”
—Ralph Waldo Emerson (1803–1882)
“There must be no cessation
Of motion, or of the noise of motion,
The renewal of noise
And manifold continuation....”
—Wallace Stevens (1879–1955)
“They had met, and included in their meeting the thrust of the manifold grass stems, the cry of the peewit, the wheel of the stars.”
—D.H. (David Herbert)