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# Image (mathematics)

In mathematics, an image is the subset of a function's codomain which is the output of the function from a subset of its domain. [1]

## Bijection, injection and surjection

In mathematics, injections, surjections and bijections are classes of functions distinguished by the manner in which arguments (input expressions from the domain) and images (output expressions from the codomain) are related or mapped to each other.

## Binary relation

In mathematics, a binary relation on a set A is a set of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2.

## Boolean algebra (structure)

In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice.

## Cartesian product

In set theory (and, usually, in other parts of mathematics), a Cartesian product is a mathematical operation that returns a set (or product set or simply product) from multiple sets.

## Codomain

In mathematics, the codomain or target set of a function is the set into which all of the output of the function is constrained to fall.

## Concentric objects

In geometry, two or more objects are said to be concentric, coaxal, or coaxial when they share the same center or axis.

## Domain of a function

In mathematics, and more specifically in naive set theory, the domain of definition (or simply the domain) of a function is the set of "input" or argument values for which the function is defined.

## Empty set

In mathematics, and more specifically set theory, the empty set or null set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero.

## Fiber (mathematics)

In mathematics, the term fiber (or fibre in British English) can have two meanings, depending on the context.

## Fiber bundle

In mathematics, and particularly topology, a fiber bundle (or, in British English, fibre bundle) is a space that is locally a product space, but globally may have a different topological structure.

## Function (mathematics)

In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.

## Image (category theory)

In category theory, a branch of mathematics, the image of a morphism is a generalization of the image of a function.

## Intersection (set theory)

In mathematics, the intersection A ∩ B of two sets A and B is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements.

## Inverse function

In mathematics, an inverse function (or anti-function) is a function that "reverses" another function: if the function applied to an input gives a result of, then applying its inverse function to gives the result, and vice versa.

## Kernel (set theory)

In set theory, the kernel of a function f may be taken to be either.

## Lattice (order)

A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra.

## Level set

In mathematics, a level set of a real-valued function ''f'' of ''n'' real variables is a set of the form that is, a set where the function takes on a given constant value c. When the number of variables is two, a level set is generically a curve, called a level curve, contour line, or isoline.

## Manifold

In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.

## Mathematical logic

Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics.

## Origin (mathematics)

In mathematics, the origin of a Euclidean space is a special point, usually denoted by the letter O, used as a fixed point of reference for the geometry of the surrounding space.

## Power set

In mathematics, the power set (or powerset) of any set is the set of all subsets of, including the empty set and itself, variously denoted as, 𝒫(), ℘() (using the "Weierstrass p"),,, or, identifying the powerset of with the set of all functions from to a given set of two elements,.

## Projection (mathematics)

In mathematics, a projection is a mapping of a set (or other mathematical structure) into a subset (or sub-structure), which is equal to its square for mapping composition (or, in other words, which is idempotent).

## Range (mathematics)

In mathematics, and more specifically in naive set theory, the range of a function refers to either the codomain or the image of the function, depending upon usage.

## Semilattice

In mathematics, a join-semilattice (or upper semilattice) is a partially ordered set that has a join (a least upper bound) for any nonempty finite subset.

## Set (mathematics)

In mathematics, a set is a collection of distinct objects, considered as an object in its own right.

## Set inversion

In mathematics, set inversion is the problem of characterizing the preimage X of a set Y by a function f, i.e., X.

## Set theory

Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.

## Set-builder notation

In set theory and its applications to logic, mathematics, and computer science, set-builder notation is a mathematical notation for describing a set by enumerating its elements or stating the properties that its members must satisfy.

## Singleton (mathematics)

In mathematics, a singleton, also known as a unit set, is a set with exactly one element.

## Subset

In mathematics, a set A is a subset of a set B, or equivalently B is a superset of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide.

## Tangent bundle

In differential geometry, the tangent bundle of a differentiable manifold M is a manifold TM which assembles all the tangent vectors in M. As a set, it is given by the disjoint unionThe disjoint union ensures that for any two points x1 and x2 of manifold M the tangent spaces T1 and T2 have no common vector.

## Tangent space

In mathematics, the tangent space of a manifold facilitates the generalization of vectors from affine spaces to general manifolds, since in the latter case one cannot simply subtract two points to obtain a vector that gives the displacement of the one point from the other.

## Uncountable set

In mathematics, an uncountable set (or uncountably infinite set) is an infinite set that contains too many elements to be countable.

## Union (set theory)

In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection.

## Value (mathematics)

In mathematics, value may refer to several, strongly related notions.

## References

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