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The Krohn-Rhodes complexity, also called the group complexity or simply "the complexity," of a finite semigroup S is the smallest number of groups in a wreath product of ...

A family of subsets of a topological space such that every point has a neighborhood which intersects only a finite number of them.

A method for testing nested hypotheses. To apply the procedure, given a specific model, calculate the likelihood of observing the actual data. Then compare this likelihood to ...

A type I move (conjugation) takes AB->BA for A, B in B_n where B_n is a braid group. A type II move (stabilization) takes A->Ab_n or A->Ab_n^(-1) for A in B_n, and b_n, Ab_n, ...

The rule (F,F=>G)/G, where => means "implies," which is the sole rule of inference in propositional calculus. This rule states that if each of F and F=>G is either an axiom ...

An algebraic expression containing more than one term (cf., binomial). The term is also used to refer to a polynomial.

A continuous map f:X->Y between topological spaces is said to be null-homotopic if it is homotopic to a constant map. If a space X has the property that id_X, the identity ...

Orthogonal involution, also called absolute involution, is the involution on the line at infinity that maps orthogonal directions to each other.

A tensor notation which considers the Riemann tensor R_(lambdamunukappa) as a matrix R_((lambdamu)(nukappa)) with indices lambdamu and nukappa.

If a polynomial P(x) has a root x=a, i.e., if P(a)=0, then x-a is a factor of P(x).