surjection


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Related to surjection: bijection, Injective function

surjection

[sər′jek·shən]
(mathematics)
A mapping ƒ from a set A to a set B such that for every element b of B there is an element a of A such that ƒ (a) = b. Also known as surjective mapping.

surjection

(mathematics)
A function f : A -> B is surjective or onto or a surjection if f A = B. I.e. f can return any value in B. This means that its image is its codomain.

Only surjections have right inverses, f' : B -> A where f (f' x) = x since if f were not a surjection there would be elements of B for which f' was not defined.

See also bijection, injection.
References in periodicals archive ?
Consequently, if L(X) can be embedded into L(Y) as a locally convex subspace, then there is a linear continuous surjection T from [C.sub.p](Y) onto [C.sub.p](X).
Conversely, one can show that, given open sets U' c U, there is a surjection of the graded derivation derivation modules d(U(G)) [right arrow] d(U(U')) [8].
Let (X, [[GAMMA].sup.[alpha].sub.1]), (Y, [[GAMMA].sup.[alpha].sub.2]) be NC[alpha]TSs and f: X [left arrow] Y be a continuous surjection. If A is a neutrosophic crisp [alpha]-compact in (X, [[GAMMA].sup.[alpha].sub.1]), then so is f(A) in (Y, [[GAMMA].sup.[alpha].sub.2]).
Regarding Konai's hand, Raqs muse on "digits" in a number of ways: the work of digital photography as the preparatory work behind "Untold Intimacy"; the digits as fingers; digits relating to biometric data taken from such handprints, data which were then stored in the archive; digits as numbers which ultimately factor as the basic units which can facilitate surjection. Like Galton's spectral composites, "in every sum figured by a power a remainder haunts the calculation.
1.4 The meta-categorical Distance between Reality and Phenomenality is Different from that between Phenomenality and Reality: OM [not equal to] MO--unless by way of Surjection (Reality's singular Exception, just Reality is, in itself, the "surjective-diffeonic" Exception of itself); such that
In this section it is shown that if a real [lambda] is "sufficiently far" from [[sigma].sub.[pi]] ([J.sub.Z,[psi]]; [J.sub.X,[phi]]), then [lambda][J.sub.X,[phi]] - (i*[J.sub.Z,[psi]]i) is a surjection of X onto X*.
Following [Rea06], we study below the combinatorial properties of the surjection map defined by these simplicial fans.
Obviously, the mapping [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is surjection (many-to-one) since the choice of [b.sub.0] for solving [z.sub.2]([t.sub.2]) is not unique.
since [[pi].sub.k] is a surjection from L to [L.sub.k].
By hypothesis, [there exists] a vg-irresolute, surjection f from X onto a vg-[D.sub.1] space Y [contains as member] f(x) [not equal to] f(y).
Since [[PSI].sub.[Real part]] is surjective then [PSI]: [[lambda].sub.0] [right arrow] [[mu].sub.0] is surjection and knowing that the right cancellation property hold for the classical surjective maps, this means that m [omicron] [PSI] = n [omicron] [PSI] [??] m = n.