In mathematics, the fiber of a point y in Y under a function f : X → Y is the inverse image of {y} under f, that is, 
In a variant phrase, this is also called the fiber of f at y. It is also commonly denoted f − 1(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.
In algebraic geometry, the notion of a fiber of a morphism of schemes must be defined more carefully because in general, not every point is closed. In this case, if f : X → Y is a morphism of schemes, the fiber of a point p in Y is the fibered product 
where k(p) is the residue field at p. In the same contexts, the spelling fibre is also seen.
See also
- Fibration
- Fiber bundle
- Fiber product
- Image (category theory)
- Image (mathematics)
- Inverse relation
- Kernel (mathematics)
- Preimage attack
- Relation
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