inverse image

Noun

Meaning

inverse image (plural inverse images)

The set of points that map to a given point (or set of points) under a specified function.
Under the function given by



f
(
x
)
=

x

2




{\displaystyle f(x)=x^{2}}

, the inverse image of 4 is



{
−
2
,
2
}


{\displaystyle \{-2,2\}}

, as is the inverse image of



{
4
}


{\displaystyle \{4\}}

.

Synonyms

Examples

Equivalently, f is continuous if the inverse image of every open set is open.sfn This is an attempt to capture the intuition that there are no "jumps" or "separations" in the function. Source: Internet

Continuous functions and homeomorphisms main A function or map from one topological space to another is called continuous if the inverse image of any open set is open. Source: Internet

Given a homomorphism from an arbitrary semigroup to a semilattice, each inverse image is a (possibly empty) semigroup. Source: Internet

Thus the inverse image would be a 1-manifold with boundary. Source: Internet

We conclude that left adjoint to the inverse image functor is given by the direct image. Source: Internet

Close letter words and terms