fiber (mathematics)
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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,
f-1(y)=x ∈ X : f(x) = y
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
X⋅Y mathrmS(ec k(()
where
k(
p) is the residue field at
p.In the same contexts, the spelling
fibre is also seen.
See also
{{math-stub}}
ليف (رياضيات)Urbild (Mathematik)
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- time: 1:08pm EDT - Thu, Jul 29 2010
