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The Kronecker-Weber theorem, sometimes known as the Kronecker-Weber-Hilbert theorem, is one of the earliest known results in class field theory. In layman's terms, the ...

Gelfond's theorem, also called the Gelfond-Schneider theorem, states that a^b is transcendental if 1. a is algebraic !=0,1 and 2. b is algebraic and irrational. This provides ...

If P be a point in the plane of an equilateral triangle DeltaABC, then the lengths of line segments AP, BP, and CP correspond the sides of a triangle, which is degenerate ...

The invariance of domain theorem states that if f:M->N is a one-to-one and continuous map between n-manifolds without boundary, then f is an open map.

The fundamental theorem of arithmetic states that every positive integer (except the number 1) can be represented in exactly one way apart from rearrangement as a product of ...

The closed graph theorem states that a linear operator between two Banach spaces X and Y is continuous iff it has a closed graph, where the "graph" {(x,f(x)):x in X} is ...

Bürmann's theorem deals with the expansion of functions in powers of another function. Let phi(z) be a function of z which is analytic in a closed region S, of which a is an ...

Let the opposite sides of a convex cyclic hexagon be a, a^', b, b^', c, and c^', and let the polygon diagonals e, f, and g be so chosen that a, a^', and e have no common ...

The Gelfand-Naimark theorem states that each C^*-algebra is isometrically *-isomorphic to a closed *-subalgebra of the algebra B(H) consisting of all bounded operators acting ...

A theorem proved by É. Cartan in 1913 which classifies the irreducible representations of complex semisimple Lie algebras.