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R^n is homeomorphic to R^m iff n=m. This theorem was first proved by Brouwer.

The two-dimensional version of the ham sandwich theorem.

For a simple continued fraction x=[a_0,a_1,...] with convergents p_n/q_n, the fundamental recurrence relation is given by p_nq_(n-1)-p_(n-1)q_n=(-1)^(n+1).

The first group isomorphism theorem, also known as the fundamental homomorphism theorem, states that if phi:G->H is a group homomorphism, then Ker(phi)⊴G and ...

If M is continuous and int_a^bM(x)h(x)dx=0 for all infinitely differentiable h(x), then M(x)=0 on the open interval (a,b).

The fundamental theorem of game theory which states that every finite, zero-sum, two-person game has optimal mixed strategies. It was proved by John von Neumann in 1928. ...

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 ...

A theorem which plays a fundamental role in computer science because it is one of the main tools for showing that certain orderings on trees are well-founded. These orderings ...

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 ...

If the integral coefficients C_0, C_1, ..., C_(N-1) of the polynomial f(x)=C_0+C_1x+C_2x^2+...+C_(N-1)x^(N-1)+x^N are divisible by a prime number p, while the free term C_0 ...