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An abstract simplicial complex is a collection S of finite nonempty sets such that if A is an element of S, then so is every nonempty subset of A (Munkres 1993, p. 15).

An Achilles number is a positive integer that is powerful (in the sense that each prime factor occurs with exponent greater than one) but imperfect (in the sense that the ...

Let M(X) denote the group of all invertible maps X->X and let G be any group. A homomorphism theta:G->M(X) is called an action of G on X. Therefore, theta satisfies 1. For ...

A quantity to be added to another, also called a summand. For example, in the expression a+b+c, a, b, and c are all addends. The first of several addends, or "the one to ...

An addition chain for a number n is a sequence 1=a_0<a_1<...<a_r=n, such that each member after a_0 is the sum of two earlier (not necessarily distinct) ones. The number r is ...

An additive category is a category for which the morphism sets have the structure of Abelian groups. It satisfies some, but not all the properties of an Abelian category.

The identity element of an additive group G, usually denoted 0. In the additive group of vectors, the additive identity is the zero vector 0, in the additive group of ...

In an additive group G, the additive inverse of an element a is the element a^' such that a+a^'=a^'+a=0, where 0 is the additive identity of G. Usually, the additive inverse ...

The restricted topological group direct product of the group G_(k_nu) with distinct invariant open subgroups G_(0_nu).

Relations in the definition of a Steenrod algebra which state that, for i<2j, Sq^i degreesSq^j(x)=sum_(k=0)^(|_i/2_|)(j-k-1; i-2k)Sq^(i+j-k) degreesSq^k(x), where f degreesg ...