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A set of class representatives is a subset of X which contains exactly one element from each equivalence class.

Let A be a unital C^*-algebra, then an element u in A is called co-isometry if uu^*=1.

A map f:X-->Y is called constant with constant value y if f(x)=y for all x in X, i.e., if all elements of X are sent to same element y of Y.

If A is a unital Banach algebra where every nonzero element is invertible, then A is the algebra of complex numbers.

An addition chain for which there is a subset H of members such that each member of the chain uses the largest element of H which is less than the member.

The map which assigns every member of a set A to the same element id_A. It is identical to the identity function.

An algebra in which the associator (x,x,x)=0. The subalgebra generated by one element is associative.

The function from a given nonempty set X to the power set P(X) that maps every element x of X to the set {x}.

Let A be a C^*-algebra, then two element a,b of A are called unitarily equivalent if there exists a unitary u in A such that b=uau^*.

A presentation of a group is a description of a set I and a subset R of the free group F(I) generated by I, written <(x_i)_(i in I)|(r)_(r in R)>, where r=1 (the identity ...