Fiber (mathematics)

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In mathematics, the fiber of a point y under a function f : X → Y is the inverse image of {y} under f, that is, $f^{-1}(\{y\})=\{x \in X : f(x) = y\}$

In a variant phrase, this is also called the fiber of f at y.

In various applications, this is also called:

The preimage of y under f, or the preimage of f at y. (However, this terminology can also be used in such a way that we would speak of the preimages of subsets of Y; thus, we would say the preimage of {y} under f)
The level set of y under f, or the level set of f at y.