Definition & Betydelse | Engelska ordet BIJECTIVE

Definition av BIJECTIVE

1. (matematik) bijektiv

Exempel på hur man kan använda BIJECTIVE i en mening

• In an algebraic structure such as a group, a ring, or vector space, an automorphism is simply a bijective homomorphism of an object into itself.
• 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).
• In mathematics and more specifically in topology, a homeomorphism (from Greek roots meaning "similar shape", named by Henri Poincaré), also called topological isomorphism, or bicontinuous function, is a bijective and continuous function between topological spaces that has a continuous inverse function.
• In mathematics, a permutation group is a group G whose elements are permutations of a given set M and whose group operation is the composition of permutations in G (which are thought of as bijective functions from the set M to itself).
• The epimorphisms in Set are the surjective maps, the monomorphisms are the injective maps, and the isomorphisms are the bijective maps.
• The term surjective and the related terms injective and bijective were introduced by Nicolas Bourbaki, a group of mainly French 20th-century mathematicians who, under this pseudonym, wrote a series of books presenting an exposition of modern advanced mathematics, beginning in 1935.
• In combinatorial mathematics, the theory of combinatorial species is an abstract, systematic method for deriving the generating functions of discrete structures, which allows one to not merely count these structures but give bijective proofs involving them.
• For example, supposing there are K basic symbols, an alternative Gödel numbering could be constructed by invertibly mapping this set of symbols (through, say, an invertible function h) to the set of digits of a bijective base-K numeral system.
• The generalization of the Zariski topology to the set of prime ideals of a commutative ring follows from Hilbert's Nullstellensatz, that establishes a bijective correspondence between the points of an affine variety defined over an algebraically closed field and the maximal ideals of the ring of its regular functions.
• One bijective conformal map from the open unit disk to the open upper half-plane is the Möbius transformation.
• In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed to be bijective.
• There are natural bijective correspondences between the set of valuation rings of K/k, the set of places of K/k, and the set of discrete valuations of K/k.
• The monomorphisms in Ab are the injective group homomorphisms, the epimorphisms are the surjective group homomorphisms, and the isomorphisms are the bijective group homomorphisms.
• A functor F : C → D yields an isomorphism of categories if and only if it is bijective on objects and on morphism sets.
• Lipschitz distance between metric spaces is the infimum of numbers r such that there is a bijective bi-Lipschitz map between these spaces with constants exp(-r), exp(r).
• An alternative bijective proof, given by Aigner and Ziegler and credited by them to André Joyal, involves a bijection between, on the one hand, n-node trees with two designated nodes (that may be the same as each other), and on the other hand, n-node directed pseudoforests.
• In mathematics, the isometry group of a metric space is the set of all bijective isometries (that is, bijective, distance-preserving maps) from the metric space onto itself, with the function composition as group operation.
• Another bijective proof, by André Joyal, finds a one-to-one transformation between n-node trees with two distinguished nodes and maximal directed pseudoforests.
• The function is bijective (one-to-one and onto, one-to-one correspondence, or invertible) if each element of the codomain is mapped to by exactly one element of the domain; that is, if the function is both injective and surjective.
• Then coalgebras for the endofunctor P(A×(-)) are in bijective correspondence with labelled transition systems, and homomorphisms between coalgebras correspond to functional bisimulations between labelled transition systems.

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