preimage

== English == === Etymology === From pre- + image. === Pronunciation === Rhymes: -ɪmɪdʒ === Noun === preimage (plural preimages) (mathematics) For a given function, the set of all elements of the domain that are mapped into a given subset of the codomain; (formally) given a function ƒ : X → Y and a subset B ⊆ Y, the set ƒ−1(B) = {x ∈ X : ƒ(x) ∈ B}. 1967 [Academic Press], Francois Treves, Topological Vector Spaces, Distributions and Kernels, 2006, Dover, page 22, The preimage of a neighborhood U of 0 in E must be a neighborhood of (0,x), since (0,x) is mapped into 0. ==== Synonyms ==== (set of all elements that map into a given subset of the codomain of a function): inverse image ==== Hyponyms ==== (set of all elements that map into a given subset of the codomain of a function): kernel ==== Derived terms ==== preimage attack ==== Related terms ==== image ==== Translations ==== === Further reading === Image (mathematics) on Wikipedia.Wikipedia Kernel (linear algebra) on Wikipedia.Wikipedia