preimage

preimage englanniksi

1. For a given function, the set of all elements of the domain that are mapped into a given subset of the codomain; given a function ƒ : ''X'' → ''Y'' and a subset ''B'' ⊆ ''Y'', the set ƒ−1(''B'') = {''x'' ∈ ''X'' : ƒ(''x'') ∈ ''B''}.

3. 1967 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.

4. {{quote-book|en|year=2003|author=Sergei K. Lando; Alexander K. Zvonkin|title=Graphs on Surfaces and Their Applications|pageurl=https://books.google.com.au/books?id=DMJKJdBLviwC&pg=PA56&dq=%22preimage%22%7C%22preimages%22&hl=en&sa=X&ved=0ahUKEwjiz4ay6pbbAhUD12MKHQ_LDOkQ6AEIxQEwHQv=onepage&q=%22preimage%22%7C%22preimages%22&f=false|page=56|publisher=Springer

5. {{quote-book|en|year=2005|author=Oded Goldreich|title=Foundations of Cryptography: A Primer|publisher=now Publishers|pageurl=https://books.google.com.au/books?id=1u7j2ljt0bQC&pg=PA24&dq=%22preimage%22%7C%22preimages%22&hl=en&sa=X&ved=0ahUKEwjiz4ay6pbbAhUD12MKHQ_LDOkQ6AEIwAEwHAv=onepage&q=%22preimage%22%7C%22preimages%22&f=false|page=24