Definition, Meaning, Synonyms & Anagrams | English word CODOMAIN

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Definitions of CODOMAIN

1. (mathematics, analysis) The target set into which a function is formally defined to map elements of its domain; the set denoted Y in the notation f : X → Y.

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Examples of Using CODOMAIN in a Sentence

• In mathematics, a binary relation associates elements of one set called the domain with elements of another set called the codomain.
• A bijection, bijective function, or one-to-one correspondence between two mathematical sets is a function such that each element of the second set (the codomain) is the image of exactly one element of the first set (the domain).
• More specifically, a binary operation on a set is a binary function whose two domains and the codomain are the same set.
• The French word sur means over or above, and relates to the fact that the image of the domain of a surjective function completely covers the function's codomain.
• The codomain affects whether a function is a surjection, in that the function is surjective if and only if its codomain equals its image.
• Of course, the right side of this equation doesn't make sense in typed logic unless the domain type of F matches the codomain type of G, so this is required for the composition to be defined.
• If a continuous bijection has as its domain a compact space and its codomain is Hausdorff, then it is a homeomorphism.
• Cokernels are dual to the kernels of category theory, hence the name: the kernel is a subobject of the domain (it maps to the domain), while the cokernel is a quotient object of the codomain (it maps from the codomain).
• A function is said to be an equivariant map when its domain and codomain are acted on by the same symmetry group, and when the function commutes with the action of the group.
• If g is an essential monomorphism with domain X and an injective codomain G, then G is called an injective hull of X.
• For instance, simplicial sets are contravariant with the codomain category being the category of sets.
• 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.
• This example can be extended into a general theorem about the existence of discontinuous linear maps on any infinite-dimensional normed space (as long as the codomain is not trivial).
• Pointwise operations inherit such properties as associativity, commutativity and distributivity from corresponding operations on the codomain.
• The left residual of two relations is defined presuming that they have the same domain (source), and the right residual presumes the same codomain (range, target).
• Uniform Cauchy convergence and pointwise convergence of a subsequence imply uniform convergence of the sequence, and if the codomain is complete, then uniform Cauchy convergence implies uniform convergence.
• Essential monomorphisms in a category of modules are those whose image is an essential submodule of the codomain.
• A pointed map is then a map which preserves basepoints; that is, it sends the basepoint of the domain to that of the codomain.

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