## 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:

“Odysseus saw the sirens; they were charming,

Blonde, with snub breasts and little neat posteriors,”

—John Streeter *Manifold* (b. 1915)

“Civilisation is hooped together, brought

Under a rule, under the semblance of peace

By *manifold* illusion....”

—William Butler Yeats (1865–1939)

“She ran down the stair

A twelve-year-old darling

And laughing and calling

She tossed her bright hair;”

—John Streeter *Manifold* (b. 1915)