(fixed-form theorem)
1Atiyah–Bott fixed-point theorem — In mathematics, the Atiyah–Bott fixed point theorem, proven by Michael Atiyah and Raoul Bott in the 1960s, is a general form of the Lefschetz fixed point theorem for smooth manifolds M , which uses an elliptic complex on M . This is a system of… …
2Kakutani fixed point theorem — In mathematical analysis, the Kakutani fixed point theorem is a fixed point theorem for set valued functions. It provides sufficient conditions for a set valued function defined on a convex, compact subset of a Euclidean space to have a fixed… …
3Banach fixed-point theorem — In mathematics, the Banach fixed point theorem (also known as the contraction mapping theorem or contraction mapping principle) is an important tool in the theory of metric spaces; it guarantees the existence and uniqueness of fixed points of… …
4Lefschetz fixed-point theorem — In mathematics, the Lefschetz fixed point theorem is a formula that counts the number of fixed points of a continuous mapping from a compact topological space X to itself by means of traces of the induced mappings on the homology groups of X . It …
5Fixed point (mathematics) — Not to be confused with a stationary point where f (x) = 0. A function with three fixed points In mathematics, a fixed point (sometimes shortened to fixpoint, also known as an invariant point) of a function is a point[1] that is …
6Knaster–Tarski theorem — In the mathematical areas of order and lattice theory, the Knaster–Tarski theorem, named after Bronisław Knaster and Alfred Tarski, states the following:: Let L be a complete lattice and let f : L → L be an order preserving function. Then the set …
7Atiyah–Singer index theorem — In the mathematics of manifolds and differential operators, the Atiyah–Singer index theorem states that for an elliptic differential operator on a compact manifold, the analytical index (closely related to the dimension of the space of solutions) …
8Pythagorean theorem — See also: Pythagorean trigonometric identity The Pythagorean theorem: The sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c) …
9Circle packing theorem — Example of the circle packing theorem on K5, the complete graph on five vertices, minus one edge. The circle packing theorem (also known as the Koebe–Andreev–Thurston theorem) describes the possible tangency relations between circles in the plane …
10Perron–Frobenius theorem — In linear algebra, the Perron–Frobenius theorem, proved by Oskar Perron (1907) and Georg Frobenius (1912), asserts that a real square matrix with positive entries has a unique largest real eigenvalue and that the corresponding… …
