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 $\\rightarrowtail$ or $\\

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

Sep 7, 2017 · This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have …

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 homomorphism …

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?

$ (g \circ f)$ is bijective $\rightarrow$ $f$ is bijective, $f: X \rightarrow Y$ $\hspace {.5cm} g:Y\rightarrow Z$ All of the domains and codomains here are supposed to be the real numbers.

Apr 1, 2015 · Now, I believe the function must be surjective i.e. onto, to have an inverse, since if it is not surjective, the function's inverse's domain will have some elements left out which are not mapped to …

Apr 7, 2019 · Why are permutations defined as bijective? Ask Question Asked 6 years, 8 months ago Modified 4 years, 5 months ago

Dec 12, 2014 · If you are talking just about sets, with no structure, the two concepts are identical. Usually the term "isomorphism" is used when there is some additional structure on the set. For …