To prove a function is bijective, you need to prove that it is injective and also surjective. "Injective" means no two elements in the domain of the function gets mapped to the same image.

Update: In the category of sets, an epimorphism is a surjective map and a monomorphism is an injective map. As is mentioned in the morphisms question, the usual notation is …

Sep 3, 2017 · I know that in order for a function to be invertible, it must be bijective, but does that mean that all bijective functions are invertible?

Jun 26, 2015 · Wikipedia states that "a bijective continuous map is a homeomorphism if and only if it is open, or equivalently, if and only if it is closed.". How do we prove this fact?

Jun 20, 2019 · In categories of algebras yes, a morphism that is bijective on underlying sets is always an isomorphism (invertible morphism). You want to restrict to algebras-and-operations, …

Example where $f\circ g$ is bijective, but neither $f$ nor $g$ is bijective Ask Question Asked 13 years, 3 months ago Modified 1 year, 11 months ago

Nov 22, 2021 · What's the difference between Injective and Bijective? For example, is there a more rigorous proof of the bijectivity of a function? Also, can these properties be applied to …

The point being that the bijective property should actually refer to the "one-to-one" nature of the relation or function in question. (Functions get uniquely defined 'for free'. The extra ingredient …

Jun 19, 2017 · $f$ is a homeomorphism iff $f$ is bijective, continuous and open Ask Question Asked 8 years, 6 months ago Modified 3 years, 5 months ago

Jan 3, 2017 · The question is simple : consider the family of monotonic functions ; m(x): R → R m (x): R → R, and the familly of bijective functions ; b(x):R →R b (x): R → R. Are they actually …