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Surjection


Surjection

Let f be a function defined on a set A and taking values in a set B. Then f is said to be a surjection (or surjective map) if, for any b in B, there exists an a in A for which b=f(a). A surjection is sometimes referred to as being "onto."

Let the function be an operator which maps points in the domain to every point in the range and let V be a vector space with A,B in V. Then a transformation T defined on V is a surjection if there is an A in V such that T(A)=B for all B.

In the categories of sets, groups, modules, etc., an epimorphism is the same as a surjection, and is used synonymously with "surjection" outside of category theory.


See also

Bijection, Domain, Epimorphism, Injection, Many-to-One, Range

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Cite this as:

Weisstein, Eric W. "Surjection." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Surjection.html

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