Bijective Function

up:: 020 MOC Mathematics

A function $f:X\to Y$ is said to be bijective if it induces a one-to-one correspondence between $X$ and $Y$. That is,

$$\forall y\in Y,\exists !x\in X\mid f(x)=y$$

That is, $f$ is both an Injective Function and a Surjective Function.

Appearance in Mathematics

• A function that is both a bijection and a group homomorphism is called a Group Isomorphism
• A function that is both a bijection and a continuous function in both directions is said to be a Homeomorphism