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)
“She ran down the stair
A twelve-year-old darling
And laughing and calling
She tossed her bright hair;”
—John Streeter Manifold (b. 1915)
“The Lord wrote it all down on the little slate
Of the baby tortoise.
Outward and visible indication of the plan within,
The complex, manifold involvedness of an individual creature”
—D.H. (David Herbert)