(mathematics) A theorem stating that, if L is a complete lattice and f : L → L is an order-preserving function, then the set of fixed points of f in L is also a complete lattice. It has important applications in formal semantics of programming languages and abstract interpretation.

(combinatorial game theory) A theorem stating that every impartial game under the normal play convention is equivalent to a nimber.

(mathematics) A theorem in operator theory, stating that, if T is a contraction on a Hilbert space H, and U is its minimal unitary dilation acting on some Hilbert space K, and R is an operator on H commuting with T, then there is an operator S on K commuting with U such that RTⁿ=P_HSUⁿ|_H;∀n≥0, and ‖S‖=‖R‖. In other words, an operator from the commutant of T can be "lifted" to an operator in the commutant of the unitary dilation of T.

(mathematics) A basic result of complex manifold theory and complex algebraic geometry, describing general conditions under which sheaf cohomology groups with indices q > 0 are automatically zero.

(mathematics, functional analysis) A proposition about convex sets in topological vector spaces.

(mathematics) An important theorem on the existence and uniqueness of solutions to first-order equations with given initial conditions.

(mathematics) A theorem stating that, given n measurable "objects" in n-dimensional Euclidean space, it is possible to divide all of them in half (with respect to their measure, i.e. volume) with a single (n−1)-dimensional hyperplane.

(mathematics, physics) A theorem about certain vector spaces, relating to string theory.

(graph theory) A theorem stating that given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colors are required to color the regions so that no two adjacent regions have the same color (adjacent being defined as two regions sharing a boundary, not counting corners, in which three or more regions share a boundary).

(mathematics) In knot theory, a theorem stating that three-dimensional smooth curves with small total curvature must be unknotted.