Synonymer & Information om | Engelska ordet SURJECTIVE

Exempel på hur man kan använda SURJECTIVE i en mening

• For example, the division example above is surjective (or onto) because every rational number may be expressed as a quotient of an integer and a natural number.
• 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.
• The codomain affects whether a function is a surjection, in that the function is surjective if and only if its codomain equals its image.
• Many authors in abstract algebra and universal algebra define an epimorphism simply as an onto or surjective homomorphism.
• A normable space is reflexive if and only if it is semi-reflexive or equivalently, if and only if the evaluation map is surjective.
• Open mapping theorem (topological groups), states that a surjective continuous homomorphism of a locally compact Hausdorff group G onto a locally compact Hausdorff group H is an open mapping if G is σ-compact.
• For example, if f : M → M is a surjective R-endomorphism of a finitely generated module M, then f is also injective, and hence is an automorphism of M.
• This means that P is projective if and only if this functor preserves epimorphisms (surjective homomorphisms), or if it preserves finite colimits.
• The monomorphisms in Ab are the injective group homomorphisms, the epimorphisms are the surjective group homomorphisms, and the isomorphisms are the bijective group homomorphisms.
• An isogeny between algebraic groups is a surjective morphism with finite kernel; two tori are said to be isogenous if there exists an isogeny from the first to the second.
• The Stein factorization theorem states that any proper morphism to a locally noetherian scheme can be factored as X → Z → Y, where X → Z is proper, surjective, and has geometrically connected fibers, and Z → Y is finite.
• Given an abelian category A and a Serre subcategory B, one can define the quotient category A/B, which is an abelian category equipped with an exact functor from A to A/B that is essentially surjective and has kernel B.
• In the dual point of view, an injective map corresponds to a surjection of sheaves, and a surjective map corresponds to an injection of sheaves.
• The category of sheaves of abelian groups on a topological space X is an abelian category, and so it makes sense to ask when a morphism f: B → C of sheaves is injective (a monomorphism) or surjective (an epimorphism).
• A central isogeny of reductive groups is a surjective homomorphism with kernel a finite central subgroup scheme.
• For any smooth projective curve X with a k-rational point, the degree homomorphism is surjective, and the kernel is isomorphic to the group of k-points on the Jacobian variety of X, which is an abelian variety of dimension equal to the genus of X.
• 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.
• This numbering will be surjective (like all numberings) but not injective: there will be distinct numbers that map to the same recursively enumerable set under W.
• In the case of the unit disk, Teichmüller theory implies that the homomorphism carries quasiconformal homeomorphisms of the disk onto the group of quasi-Möbius homeomorphisms of the circle (using for example the Ahlfors–Beurling or Douady–Earle extension): it follows that the homomorphism from the quasi-isometry group into the quasi-Möbius group is surjective.

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