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 …

Jun 19, 2017 · $f$ is a homeomorphism iff $f$ is bijective, continuous and open Ask Question Asked 8 years, 4 months ago Modified 3 years, 3 months ago

Apr 15, 2020 · An isomorphism is a bijective homomorphism. I.e. there is a one to one correspondence between the elements of the two sets but there is more than that because of …

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 …

Sep 7, 2017 · Injective is where there are more x values than y values and not every y value has an x value but every x value has one y value. Surjective is where there are more x values than …

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 20, 2019 · For some other structures, such as topological spaces and differentiable manifolds, a bijective homomorphism may not be an isomorphism. Are there characterizations of sub …

Let f : A → B and g : B → C be bijections. Prove that g f : A → C is a bijection Can someone show me the steps I should take to solve this problem?

Example where $f\circ g$ is bijective, but neither $f$ nor $g$ is bijective Ask Question Asked 13 years, 1 month ago Modified 1 year, 9 months ago