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Surjective Function

Jun 29, 20231 min read

A function is said to be surjective if it covers its entire codomain . That is,

020 MOC Mathematics
065 MOC Matemática em Economia
A linear transformation between spaces of equal dimension is injective iff it's surjective iff it's an isomorphism
A surjective function is an epimorphism in the category Set
An affine map is an affine isomorphism iff its underlying linear map is an isomorphism
An endomorphism is injective iff it's surjective
Bijective Function
Epimorphism
Every function is surjective with respect to its image
Every vector space with same dimension are isomorphic to each other
Fixing a point in an affine space induces a vector space
Injective functions are bijective with respect to their image
The surjective image of the preimage of a set is equal to the set
Vector Space Isomorphism

Nicholas Funari Voltani