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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 ...

Let Q(x) be a real or complex piecewise-continuous function defined for all values of the real variable x and that is periodic with minimum period pi so that Q(x+pi)=Q(x). ...

The product of three translations along the directed sides of a triangle through twice the lengths of these sides is the identity map.

A theorem that guarantees that the trajectory of Langton's ant is unbounded.

Jackson's theorem is a statement about the error E_n(f) of the best uniform approximation to a real function f(x) on [-1,1] by real polynomials of degree at most n. Let f(x) ...

Due to Euler's prolific output, there are a great number of theorems that are know by the name "Euler's theorem." A sampling of these are Euler's displacement theorem for ...

The Banach-Steinhaus theorem is a result in the field of functional analysis which relates the "size" of a certain subset of points defined relative to a family of linear ...

A generalization of Turán's theorem to non-complete graphs.

For an n-dimensional map, the Lyapunov characteristic exponents are given by sigma_i=lim_(N->infty)ln|lambda_i(N)| for i=1, ..., n, where lambda_i is the Lyapunov ...

Alexandrov's theorem addresses conditions under which a polygon will fold into a convex polyhedron (Malkevitch).