Search results
Results From The WOW.Com Content Network
Bijective composition: the first function need not be surjective and the second function need not be injective. A function is bijective if it is both injective and surjective. A bijective function is also called a bijection or a one-to-one correspondence (not to be confused with one-to-one function, which refers to injection
Any surjective function induces a bijection defined on a quotient of its domain by collapsing all arguments mapping to a given fixed image. More precisely, every surjection f : A → B can be factored as a projection followed by a bijection as follows.
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).
Variations of the horizontal line test can be used to determine whether a function is surjective or bijective: The function f is surjective (i.e., onto) if and only if its graph intersects any horizontal line at least once. f is bijective if and only if any horizontal line will intersect the graph exactly once.
A faithful functor need not be injective on objects or morphisms. That is, two objects X and X′ may map to the same object in D (which is why the range of a full and faithful functor is not necessarily isomorphic to C), and two morphisms f : X → Y and f′ : X′ → Y′ (with different domains/codomains) may map to the same morphism in D.
Because a function is trivially surjective when restricted to its image, the term partial bijection denotes a partial function which is injective. [1] An injective partial function may be inverted to an injective partial function, and a partial function which is both injective and surjective has an injective function as inverse.
Like any other bijection, a global isometry has a function inverse. The inverse of a global isometry is also a global isometry. The inverse of a global isometry is also a global isometry. Two metric spaces X and Y are called isometric if there is a bijective isometry from X to Y .
is a bijection (one-to-one and onto), is continuous, the inverse function is continuous (is an open mapping). A homeomorphism is sometimes called a bicontinuous function. If such a function exists, and are homeomorphic.