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单词 Surjective
释义

surjective


A function f:XY is called surjectivePlanetmathPlanetmath or onto if, for every yY, there is an xX such that f(x)=y.

Equivalently, f:XY is onto when its image is all the codomain:

Imf=Y.

Properties

  1. 1.

    If f:XY is any function, then f:Xf(X) isa surjection. That is, by restricting the codomain,any function induces a surjection.

  2. 2.

    The compositionMathworldPlanetmath of surjective functions (when defined) isagain a surjective function.

  3. 3.

    If f:XY is a surjection and BY, then(see this page (http://planetmath.org/InverseImage))

    ff-1(B)=B.
Titlesurjective
Canonical nameSurjective
Date of creation2013-03-22 12:32:48
Last modified on2013-03-22 12:32:48
Ownerdrini (3)
Last modified bydrini (3)
Numerical id7
Authordrini (3)
Entry typeDefinition
Classificationmsc 03-00
Synonymonto
Related topicTypesOfHomomorphisms
Related topicInjectiveFunction
Related topicBijection
Related topicFunction
Related topicOneToOneFunctionFromOntoFunction
Definessurjection
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更新时间:2025/5/4 15:39:25