Fiber (mathematics)

Fiber (mathematics)

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".

In the same contexts, the spelling fibre is also seen.

ee also

* Fibration
* Fiber bundle
* Fiber product
* Image (category theory)
* Image (mathematics)
* Inverse relation
* Preimage attack
* Relation


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