# Definition: Surjective Function

A function $$f:A\mapsto B$$ is called surjective (or surjection), if for every $$y\in B$$ there is an $$x\in A$$ with $$f(x)=b$$. This corresponds to the right-total property, in addition to its the properties of a function. ### Notes

• A surjective function aims at every element $b\in B.$
• In other words, every element $b\in B$ has a fiber.
• In other words, the image $f(A)$ is the whole set $B.$

Definitions: 1 2 3 4 5
Explanations: 6 7
Proofs: 8 9 10 11 12 13 14 15 16 17 18 19 20
Propositions: 21 22 23 24
Solutions: 25

Github: non-Github:
@Brenner

### References

#### Bibliography

1. Knauer Ulrich: "Diskrete Strukturen - kurz gefasst", Spektrum Akademischer Verlag, 2001
2. Reinhardt F., Soeder H.: "dtv-Atlas zur Mathematik", Deutsche Taschenbuch Verlag, 1994, 10th Edition
3. Kane, Jonathan: "Writing Proofs in Analysis", Springer, 2016

#### Adapted from CC BY-SA 3.0 Sources:

1. Brenner, Prof. Dr. rer. nat., Holger: Various courses at the University of Osnabrück