Also found in: Dictionary, Wikipedia.


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 ?
In fact, for each group G, there is a universal inverse semigroup S(G), nowadays known as Exel's semigroup, which associates to each partial action of G on a set (topological space) X, a morphism of semigroups between S(G) and the inverse semigroup of partially defined bijections (homeomorphisms) in X.
One of the main reasons being that they are in bijection with permutations.
The bijection [chi] : [sigma] [right arrow] [([[sigma].
Let S is a right normal orthodox semigroup with an inverse transversal S[degrees], Blyth and Almeida Snatos in [4] proved that there is an order-preserving bijection from the set of all locally maximal S[degrees]-cones to the set of all left amenable orders definable on S and the natural partial order is the smallest left amenable partial order(see theorems 7 and 11 in [4]).
Real part]] is bijection fuzzy map, but the converse not necessarily true.
The bijection preserves inclusions and normality, so it is effectively perfect.
This clearly define a bijection or relation of equivalence between the hidden variables [[[lambda].
It can be shown [2] that there is a bijection between the set of expected values, [mu], and the set of natural parameters, [theta].
A graph G with q edges and p vertices is said to be edge graceful if there exists a bijection f from the edge set to the set {1,2, .
Following Lewin (1987, 46-50), transposition in a commutative GIS is seen as an "interval-preserving" bijection from one set onto another.
Since there is a natural bijection between substitutions and sets of equations in solved form, such parallel composition was defined in terms of "solving" the equations associated with the substitutions being composed.
The points of this line are in bijection with the isomorphism classes of elliptic curves over F (via the j-invariant).