Search results
Results From The WOW.Com Content Network
exceptional inverse image Rf! : D(Sh(Y)) → D(Sh(X)). The exclamation mark is often pronounced "shriek" (slang for exclamation mark), and the maps called "f shriek" or "f lower shriek" and "f upper shriek"—see also shriek map. The exceptional inverse image is in general defined on the level of derived categories only.
The traditional notations used in the previous section do not distinguish the original function : from the image-of-sets function : (); likewise they do not distinguish the inverse function (assuming one exists) from the inverse image function (which again relates the powersets). Given the right context, this keeps the notation light and ...
In mathematics, specifically in algebraic topology and algebraic geometry, an inverse image functor is a contravariant construction of sheaves; here “contravariant” in the sense given a map :, the inverse image functor is a functor from the category of sheaves on Y to the category of sheaves on X.
Using the language of category theory, the composition operator is a pull-back on the space of measurable functions; it is adjoint to the transfer operator in the same way that the pull-back is adjoint to the push-forward; the composition operator is the inverse image functor.
Every normal function f has arbitrarily large fixed points; see the fixed-point lemma for normal functions for a proof. One can create a normal function f ′ : Ord → Ord, called the derivative of f, such that f ′(α) is the α-th fixed point of f. [2] For a hierarchy of normal functions, see Veblen functions.
In mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f. The inverse of f exists if and only if f is bijective , and if it exists, is denoted by f − 1 . {\displaystyle f^{-1}.}
The local inverse is a kind of inverse function or matrix inverse used in image and signal processing, as well as in other general areas of mathematics. The concept of a local inverse came from interior reconstruction of CT [clarification needed] images. One interior reconstruction method first approximately reconstructs the image outside the ...
An involution is a function f : X → X that, when applied twice, brings one back to the starting point. In mathematics, an involution, involutory function, or self-inverse function [1] is a function f that is its own inverse, f(f(x)) = x. for all x in the domain of f. [2] Equivalently, applying f twice produces the original value.