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A mapping ƒ from a set A onto a set B which is both an injection and a surjection; that is, for every element b of B there is a unique element a of A for which ƒ (a) = b. Also known as bijective mapping.


A function is bijective or a bijection or a one-to-one correspondence if it is both injective (no two values map to the same value) and surjective (for every element of the codomain there is some element of the domain which maps to it). I.e. there is exactly one element of the domain which maps to each element of the codomain.

For a general bijection f from the set A to the set B:

f'(f(a)) = a where a is in A and f(f'(b)) = b where b is in B.

A and B could be disjoint sets.

See also injection, surjection, isomorphism, permutation.
References in periodicals archive ?
Since g is also a bijective map g(y) = x for all y [member of] Y satisfying the conditions:
Then there exists a bijective map from [LAMBDA] to X which maps [LAMBDA]-closed sets in [LAMBDA] to closed nowhere dense sets in X.
We abbreviate a bijective map preserving closed nowhere dense sets as cln-bijection.
f:X [right arrow] Y is a bijective map defined by: f(x) = y for all x [member of] X satisfying the conditions:
Hua's fundamental theorem of geometry of matrices describes the general form of bijective maps on the space of all m X n matrices over a division ring D that preserve adjacency in both directions, explains Semrl.