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What is a preimage?

What is a preimage? Here are some definitions.

Noun
  1. (mathematics) The set containing exactly every member of the domain of a function such that the member is mapped by the function onto an element of a given subset of the codomain of the function. Formally, of a subset B of the codomain Y under a function ƒ, the subset of the domain X defined by
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Examples
Security criteria for hash functions include collision resistance and preimage resistance and so on.
A function between topological spaces is semi-strongly continuous provided the preimage of each semi-open set is open.
Now we shall define the image and preimage of intuitionistic fuzzy sets.
So, the preimage of the basis, the columns of U, are assumed to be known.

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