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Let z be defined as a function of w in terms of a parameter alpha by z=w+alphaphi(z). (1) Then Lagrange's inversion theorem, also called a Lagrange expansion, states that any ...

In functional analysis, the Banach-Alaoglu theorem (also sometimes called Alaoglu's theorem) is a result which states that the norm unit ball of the continuous dual X^* of a ...

The Diophantine equation x^2+y^2=p can be solved for p a prime iff p=1 (mod 4) or p=2. The representation is unique except for changes of sign or rearrangements of x and y. ...

If X is a locally compact T2-space, then the set C_ degrees(X) of all continuous complex valued functions on X vanishing at infinity (i.e., for each epsilon>0, the set {x in ...

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 ...

In the field of functional analysis, the Krein-Milman theorem is a result which characterizes all (nonempty) compact convex subsets K of "sufficiently nice" topological ...

If X is any space, then there is a CW-complex Y and a map f:Y->X inducing isomorphisms on all homotopy, homology, and cohomology groups.

The extended mean-value theorem (Anton 1984, pp. 543-544), also known as the Cauchy mean-value theorem (Anton 1984, pp. 543) and Cauchy's mean-value formula (Apostol 1967, p. ...

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 ...