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Etymologie

Was (wer) ist injective mapping - definition

FUNCTION THAT PRESERVES DISTINCTNESS

Injective; One to one function; Injection (mathematics); One-to-one function; Injectivity; Injective mapping; Injective map; 1 to 1; Injective Function; ↣; Into relation; One-to-one mapping; One-to-one correlation; Onetoone; Injection function

Injective hull

NOTION IN ABSTRACT ALGEBRA

Module of finite rank; Injective envelope

In mathematics, particularly in algebra, the injective hull (or injective envelope) of a module is both the smallest injective module containing it and the largest essential extension of it. Injective hulls were first described in .

https://en.wikipedia.org/wiki/Injective_hull

Collaborative mapping

AGGREGATION OF WEB MAPS AND USER-GENERATED CONTENT, FROM A GROUP OF INDIVIDUALS OR ENTITIES, AND CAN TAKE SEVERAL DISTINCT FORMS

Collaborative Mapping; Citizen mapping

Collaborative mapping is the aggregation of Web mapping and user-generated content, from a group of individuals or entities, and can take several distinct forms. With the growth of technology for storing and sharing maps, collaborative maps have become competitors to commercial services, in the case of OpenStreetMap, or components of them, as in Google Map Maker and Yandex.

https://en.wikipedia.org/wiki/Collaborative_mapping

Brain mapping

IMAGING TECHNIQUES USED TO COLOCALIZE SITES OF BRAIN FUNCTIONS OR PHYSIOLOGICAL ACTIVITY WITH BRAIN STRUCTURES

Brain Mapping; Brain map

Brain mapping is a set of neuroscience techniques predicated on the mapping of (biological) quantities or properties onto spatial representations of the (human or non-human) brain resulting in maps.

https://en.wikipedia.org/wiki/Brain_mapping

Wikipedia

Injective function

In mathematics, an injective function (also known as injection, or one-to-one function) is a function f that maps distinct elements of its domain to distinct elements; that is, f(x₁) = f(x₂) implies x₁ = x₂. (Equivalently, x₁ ≠ x₂ implies f(x₁) ≠ f(x₂) in the equivalent contrapositive statement.) In other words, every element of the function's codomain is the image of at most one element of its domain. The term one-to-one function must not be confused with one-to-one correspondence that refers to bijective functions, which are functions such that each element in the codomain is an image of exactly one element in the domain.

A homomorphism between algebraic structures is a function that is compatible with the operations of the structures. For all common algebraic structures, and, in particular for vector spaces, an injective homomorphism is also called a monomorphism. However, in the more general context of category theory, the definition of a monomorphism differs from that of an injective homomorphism. This is thus a theorem that they are equivalent for algebraic structures; see Homomorphism § Monomorphism for more details.

A function $f$ that is not injective is sometimes called many-to-one.

https://en.wikipedia.org/wiki/Injective function