Feb 24, 2017

Fiber and Preimage

In the algebra class, I encountered a concept called fiber, which sounded similar to preimage, and I didn't get the difference. According to Wikipedia, given $f: X \to Y$, the preimage of a set $B \subseteq Y$ under $f$ is a subset of $X$ defined by $f^{-1}(B)=\{\,x\in X\,|\,f(x)\in B\}$. If $B$ is a singleton set, i.e. $B = \{y\}$, the preimage $f^{−1}(y)$ is also called the fiber of $y$.