## MANIFOLD

### Manifold

In mathematics, a**manifold**is a topological space that near each point resembles 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.

*The above text is a snippet from Wikipedia: Manifold*

and as such is available under the Creative Commons Attribution/Share-Alike License.

and as such is available under the Creative Commons Attribution/Share-Alike License.

### manifold

#### Noun

- A copy made by the manifold writing process.
- A pipe fitting or similar device that connects multiple inputs or outputs.
- The third stomach of a ruminant animal, an omasum.
- A topological space that looks locally like the "ordinary" Euclidean space <math>\mathbb{R}^n</math> and is Hausdorff.

#### Verb

#### Adjective

- Various in kind or quality, diverse
*The***manifold**meanings of the simple English word 'set' are infamous among dictionary makers.

- Many in number, numerous; multiple, multiplied.
- Complicated.
- Exhibited at diverse times or in various ways.
- c1384
*... the manyfold grace of God.*— I Petre 4:10 (Wycliffe's Bible) - 1611
*The manifold wisdom of God.*— Ephesians 3:10. ()

- c1384

#### Adverb

- Many times; repeatedly.

*The above text is a snippet from Wiktionary: manifold*

and as such is available under the Creative Commons Attribution/Share-Alike License.

and as such is available under the Creative Commons Attribution/Share-Alike License.