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 ?
If [rho] [member of] Con(A), then we can consider the natural surjection [[rho].
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.
It defines a surjection k from the linear orders on V to the maximal signed spines on T: the image k( F) of a linear order f is the unique maximal signed spine on T for which F is a linear extension.
The complex (or the triple) (B, [pi], X), where B and X are topological spaces and [pi] : B [right arrow] X is a continuous open surjection, is called a fibre bundle.
On the other hand, since a factor f U [right arrow] X(f) = {f(u) | u [element of] U} is always a surjection that implies the complete factor 1 is a bijection.
be the set of all the monomorphisms (l, [LAMBDA]) : (E, p, T) [right arrow] (F, q, S) of S such that l is an embedding (homeomorphism onto its image) and [LAMBDA] is a surjection and let E be the set of all the epimorphisms (l, [LAMBDA]) : (E, p, T) [right arrow] (F, q, S) of S such that, if (a, b) [member of] F V F and a [not equal to] b then for each V [member of] V(g(a)) there is r [member of] [l.
The functor [mathematical expression omitted], respectively [mathematical expression omitted], induces a surjection
the morphism g is called a special homogeneous surjection when ([pi]1, [DELTA]) (or, equivalently, ([[pi].
2]) be NCTSs and f: X [right arrow] Y be a continuous surjection.
Since f is M-vg-open almost vg- irresolute surjection, we obtain A [subset] f(U) [subset] vg[bar.
M1) For any A [subset or equal to] E and b [member of] E\A, there exists a surjection M(A) [?
We can very empathically say that the Ultimate Observer is such that if that One stopped observing the Universe by way of Surjection (Surjectivity, Noesis), and not only in terms of phenomenological abstract laws and concrete entities, it would all cease to exist at once--at one Now--"before before" and "after after", noumenally and phenomenally.