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If J is a simple closed curve in R^2, the closure of one of the components of R^2-J is homeomorphic with the unit 2-ball. This theorem may be proved using the Riemann mapping ...

The bicommutant theorem is a theorem within the field of functional analysis regarding certain topological properties of function algebras. The theorem says that, given a ...

The Reynolds transport theorem, also called simply the Reynolds theorem, is an important result in fluid mechanics that's often considered a three-dimensional analog of the ...

The Chebotarev density theorem is a complicated theorem in algebraic number theory which yields an asymptotic formula for the density of prime ideals of a number field K that ...

Kakutani's fixed point theorem is a result in functional analysis which establishes the existence of a common fixed point among a collection of maps defined on certain ...

There are several theorems known as the "sandwich theorem." In calculus, the squeeze theorem is also sometimes known as the sandwich theorem. In graph theory, the sandwich ...

The squeeze theorem, also known as the squeezing theorem, pinching theorem, or sandwich theorem, may be stated as follows. Let there be two functions f_-(x) and f_+(x) such ...

The Heine-Borel theorem states that a subspace of R^n (with the usual topology) is compact iff it is closed and bounded. The Heine-Borel theorem can be proved using the ...

An analytic function f(z) whose Laurent series is given by f(z)=sum_(n=-infty)^inftya_n(z-z_0)^n, (1) can be integrated term by term using a closed contour gamma encircling ...

Fermat's last theorem is a theorem first proposed by Fermat in the form of a note scribbled in the margin of his copy of the ancient Greek text Arithmetica by Diophantus. The ...