Noun
preimage (plural preimages)
(mathematics) For a given function, the set of all elements of the domain that are mapped into a given subset of the codomain; (formally) given a function ƒ : X → Y and a subset B ⊆ Y, the set ƒ(B) = {x ∈ X : ƒ(x) ∈ B}.
The preimage of
{
4
,
9
}
{\displaystyle \{4,9\}}
under the function
f
:
R
→
R
:
f
(
x
)
=
x
2
{\displaystyle f:\mathbb {R} \rightarrow \mathbb {R} :f(x)=x^{2}}
is the set
{
−
3
,
−
2
,
+
2
,
+
3
}
{\displaystyle \{-3,-2,+2,+3\}}
.
A function between two measurable spaces is called a measurable function if the preimage of every measurable set is measurable. Source: Internet
For instance, a real-valued measurable function is a function for which the preimage of each Borel set is measurable. Source: Internet
Every ring homomorphism f : R → S induces a continuous map Spec(f) : Spec(S) → Spec(R) (since the preimage of any prime ideal in S is a prime ideal in R). Source: Internet
The preimage of a finite point group is called by the same name, with the prefix binary. Source: Internet
As a consequence, the preimage is not empty. Source: Internet
; Continuous : A function from one space to another is continuous if the preimage of every open set is open. Source: Internet