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Manifold vs Bifurcation - What's the difference?

manifold | bifurcation |

In mathematics|lang=en terms the difference between manifold and bifurcation

is that manifold is (mathematics) a topological space that looks locally like the "ordinary" euclidean space \mathbb{r}^n and is hausdorff while bifurcation is (mathematics) the change in the qualitative or topological structure of a given family as decribed by bifurcation theory.

As nouns the difference between manifold and bifurcation

is that manifold is (now historical) a copy made by the manifold writing process while bifurcation is (biology) a division into two branches.

As an adjective manifold

is various in kind or quality, diverse.

As an adverb manifold

is many times; repeatedly.

As a verb manifold

is to make manifold; multiply.

manifold

English

Alternative forms

* (l)

Etymology 1

From (etyl), from (etyl) .

Noun

(en noun)
  • (now historical) A copy made by the manifold writing process.
  • (mechanics) A pipe fitting or similar device that connects multiple inputs or outputs.
  • (US, regional, in the plural) The third stomach of a ruminant animal, an omasum.
  • * 1830 Anson, Somerset Co. Me., accessed 12 June 2007
  • My conjecture being right he will find the third stomach, or manifolds , the seat of difficulty.
  • (mathematics) A topological space that looks locally like the "ordinary" Euclidean space \mathbb{R}^n and is Hausdorff.
  • Derived terms
    * manifolder * (l) * (l)

    Adjective

    (en 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]. ([[w:King James Bible])
    Derived terms
    * manifold writing

    Adverb

    (en adverb)
  • Many times; repeatedly.
  • * 1590 , Edmund Spenser, The Faerie Queene , I.xii:
  • when his daughter deare he does behold, / Her dearely doth imbrace, and kisseth manifold .

    Etymology 2

    From (etyl) manifolden, from (etyl) .

    Verb

    (en verb)
  • To make manifold; multiply.
  • (printing) To multiply or reproduce impressions of by a single operation.
  • bifurcation

    Noun

    (en noun)
  • (biology) A division into two branches.
  • (by extension) Any place where one thing divides into two.
  • The act of bifurcating; branching or dividing in two.
  • Either of the forks or other branches resultant from such a division.
  • (geography) A place where two roads, tributaries etc. part or meet.
  • (nautical) The point where a channel divides when proceeding from seaward.
  • (mathematics) The change in the qualitative or topological structure of a given family as decribed by bifurcation theory.
  • (computer science) A command that executes one block or other of commands depending on the result of a condition.
  • Synonyms

    * (division into two branches) branched, branching, forked, forking

    Derived terms

    * bifurcation theory