Search results
Results from the WOW.Com Content Network
Functor. List of specific functions. v. t. e. 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. For a function , its inverse admits an explicit description: it sends each element ...
Inversive geometry. In geometry, inversive geometry is the study of inversion, a transformation of the Euclidean plane that maps circles or lines to other circles or lines and that preserves the angles between crossing curves. Many difficult problems in geometry become much more tractable when an inversion is applied.
Open and closed maps. In mathematics, more specifically in topology, an open map is a function between two topological spaces that maps open sets to open sets. [1][2][3] That is, a function is open if for any open set in the image is open in Likewise, a closed map is a function that maps closed sets to closed sets. [3][4] A map may be open ...
Political map of Europe, showing south at the top. Research suggests that north-south positions on maps have psychological consequences. In general, north is associated with richer people, more expensive real estate, and higher altitude, while south is associated with poorer people, cheaper prices, and lower altitude (the "north-south bias").
Similarly, the inverse image (or preimage) of a given subset of the codomain is the set of all elements of that map to a member of . The image of the function f {\displaystyle f} is the set of all output values it may produce, that is, the image of X {\displaystyle X} .
Logistic map. The logistic map is a polynomial mapping (equivalently, recurrence relation) of degree 2, often referred to as an archetypal example of how complex, chaotic behaviour can arise from very simple nonlinear dynamical equations.
e. In mathematics, a conformal map is a function that locally preserves angles, but not necessarily lengths. More formally, let and be open subsets of . A function is called conformal (or angle-preserving) at a point if it preserves angles between directed curves through , as well as preserving orientation. Conformal maps preserve both angles ...
Global version. The inverse function theorem is a local result; it applies to each point. A priori, the theorem thus only shows the function is locally bijective (or locally diffeomorphic of some class). The next topological lemma can be used to upgrade local injectivity to injectivity that is global to some extent.