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:
“A large city cannot be experientially known; its life is too manifold for any individual to be able to participate in it.”
—Aldous Huxley (1894–1963)
“There must be no cessation
Of motion, or of the noise of motion,
The renewal of noise
And manifold continuation....”
—Wallace Stevens (1879–1955)
“Before abstraction everything is one, but one like chaos; after abstraction everything is united again, but this union is a free binding of autonomous, self-determined beings. Out of a mob a society has developed, chaos has been transformed into a manifold world.”
—Novalis [Friedrich Von Hardenberg] (1772–1801)