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 $B.$
Mentioned in:
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
Thank you to the contributors under CC BY-SA 4.0! 
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- @Brenner
References
Bibliography
- Knauer Ulrich: "Diskrete Strukturen - kurz gefasst", Spektrum Akademischer Verlag, 2001
- Reinhardt F., Soeder H.: "dtv-Atlas zur Mathematik", Deutsche Taschenbuch Verlag, 1994, 10th Edition
- Kane, Jonathan: "Writing Proofs in Analysis", Springer, 2016
Adapted from CC BY-SA 3.0 Sources:
- Brenner, Prof. Dr. rer. nat., Holger: Various courses at the University of Osnabrück
