preimage
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See also: préimage
Contents
English[edit]
Etymology[edit]
Pronunciation[edit]
 Rhymes: ɪmɪdʒ
Noun[edit]
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}.
 The preimage of under the function is the set .
 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.
 2003, Sergei K. Lando, Alexander K. Zvonkin, Graphs on Surfaces and Their Applications, Springer, page 56,
 Previously, maps and hypermaps were constructed as the preimages of a segment joining two of the three critical values.
 2005, Oded Goldreich, Foundations of Cryptography: A Primer, now Publishers, page 24,
 Loosely speaking, saying that a function f is oneway implies that given y (in the range of f) it is infeasible to find a preimage of y under f.
Synonyms[edit]
 (set of all elements that map into a given subset of the codomain of a function): inverse image
Hyponyms[edit]
 (set of all elements that map into a given subset of the codomain of a function): kernel
Derived terms[edit]
Related terms[edit]
Translations[edit]
set of all elements that map into a given subset of the codomain of a function

Further reading[edit]
 Image (mathematics) on Wikipedia.Wikipedia
 Kernel (linear algebra) on Wikipedia.Wikipedia