manifold

manifold
—manifoldly, adv. —manifoldness, n.
/man"euh fohld'/, adj.
1. of many kinds; numerous and varied: manifold duties.
2. having numerous different parts, elements, features, forms, etc.: a manifold program for social reform.
3. using, functioning with, or operating several similar or identical devices at the same time.
4. (of paper business forms) made up of a number of sheets interleaved with carbon paper.
5. being such or so designated for many reasons: a manifold enemy.
n.
6. something having many different parts or features.
7. a copy or facsimile, as of something written, such as is made by manifolding.
8. any thin, inexpensive paper for making carbon copies on a typewriter.
9. Mach. a chamber having several outlets through which a liquid or gas is distributed or gathered.
10. Philos. (in Kantian epistemology) the totality of discrete items of experience as presented to the mind; the constituents of a sensory experience.
11. Math. a topological space that is connected and locally Euclidean. Cf. locally Euclidean space.
v.t.
12. to make copies of, as with carbon paper.
[bef. 1000; ME; OE manigf(e)ald (adj.). See MANY, -FOLD]
Syn. 1. various, multitudinous. See many. 2. varied, divers, multifarious.
Ant. 1. simple, single.

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In mathematics, a topological space (see topology) with a family of local coordinate systems related to each other by certain classes of coordinate transformations.

Manifolds occur in algebraic geometry, differential equations, and classical dynamics. They are studied for their global properties by the methods of algebra and algebraic topology and form a natural domain for the global analysis of differential equations. See also tensor analysis.

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      in mathematics, a generalization and abstraction of the notion of a curved surface; a manifold is a topological space that is modeled closely on Euclidean space locally but may vary widely in global properties. Each manifold is equipped with a family of local coordinate systems that are related to each other by coordinate transformations belonging to a specified class. Manifolds occur in algebraic and differential geometry, differential equations, classical dynamics, and relativity. They are studied for their global properties by the methods of analysis and algebraic topology, and they form natural domains for the global analysis of differential equations, particularly equations that arise in the calculus of variations. In mechanics they arise as “phase spaces”; in relativity, as models for the physical universe; and in string theory, as one- or two-dimensional membranes and higher-dimensional “branes.”

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Universalium. 2010.

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  • manifold — [ manifɔld ] n. m. • 1930; mot angl., pour manifold paper ♦ Anglic. 1 ♦ Carnet comportant plusieurs séries de feuilles et de papier carbone. 2 ♦ (1960) Techn. Ensemble de vannes et de conduits orientant un fluide vers un réservoir ou des… …   Encyclopédie Universelle

  • manifold — [man′ə fōld΄] adj. [ME < OE manigfeald: see MANY & FOLD] 1. having many and various forms, features, parts, etc. [manifold wisdom] 2. of many sorts; many and varied; multifarious: used with a plural noun [manifold duties] 3. being such in many …   English World dictionary

  • Manifold — Man i*fold, a. [AS. manigfeald. See {Many}, and {Fold}.] 1. Various in kind or quality; many in number; numerous; multiplied; complicated. [1913 Webster] O Lord, how manifold are thy works! Ps. civ. 24. [1913 Webster] I know your manifold… …   The Collaborative International Dictionary of English

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  • Manifold — Man i*fold, v. t. [imp. & p. p. {Manifolded}; p. pr. & vb. n. {Manifolding}.] To take copies of by the process of manifold writing; as, to manifold a letter. [1913 Webster] …   The Collaborative International Dictionary of English

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  • manifold — ► ADJECTIVE formal or literary 1) many and various. 2) having many different forms. ► NOUN 1) a pipe or chamber branching into several openings. 2) (in an internal combustion engine) the part conveying air and fuel from the carburettor to the… …   English terms dictionary

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