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The preimage of an output value is the set of input values that produce . More generally, evaluating f {\displaystyle f} at each element of a given subset A {\displaystyle A} of its domain X {\displaystyle X} produces a set, called the " image of A {\displaystyle A} under (or through) f {\displaystyle f} ".
Auto effective registration statement for securities of certain Canadian issuer under the Securities Act of 1933 F-10POS Post-effective amendment to a F-10EF registration F-1MEF A new registration statement filed under Rule 462(b) to add securities to a prior related effective registration statement filed on Form F-1 F-3
This function maps each image to its unique preimage. The composition of two bijections is again a bijection, but if g ∘ f {\displaystyle g\circ f} is a bijection, then it can only be concluded that f {\displaystyle f} is injective and g {\displaystyle g} is surjective (see the figure at right and the remarks above regarding injections and ...
If f : X → Y is surjective and B is a subset of Y, then f(f −1 (B)) = B. Thus, B can be recovered from its preimage f −1 (B). For example, in the first illustration in the gallery, there is some function g such that g(C) = 4. There is also some function f such that f(4) = C.
Then a pullback of f and g (in Set) is given by the preimage f −1 [B 0] together with the inclusion of the preimage in A. f −1 [B 0] ↪ A. and the restriction of f to f −1 [B 0] f −1 [B 0] → B 0. Because of this example, in a general category the pullback of a morphism f and a monomorphism g can be thought of as the "preimage" under ...
The fibers of are that line and all the straight lines parallel to it, which form a partition of the plane . More generally, if f {\displaystyle f} is a linear map from some linear vector space X {\displaystyle X} to some other linear space Y {\displaystyle Y} , the fibers of f {\displaystyle f} are affine subspaces of X {\displaystyle X ...
In mathematics, and in particular measure theory, a measurable function is a function between the underlying sets of two measurable spaces that preserves the structure of the spaces: the preimage of any measurable set is measurable.
Form S-1 is an SEC filing used by companies planning on going public to register their securities with the U.S. Securities and Exchange Commission (SEC) as the "registration statement by the Securities Act of 1933". The S-1 contains the basic business and financial information on an issuer with respect to a specific securities offering.