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The symmetry operation (x,y,z)->(x,y,-z), etc., which is equivalent to 2^_, where the bar denotes an improper rotation.

A set M of all polynomials in s variables, x_1, ..., x_s such that if P, P_1, and P_2 are members, then so are P_1+P_2 and QP, where Q is any polynomial in x_1, ..., x_s.

A basis of a modular system M is any set of polynomials B_1, B_2, ... of M such that every polynomial of M is expressible in the form R_1B_1+R_2B_2+..., where R_1, R_2, ... ...

A function periodic with period 2pi such that p(theta+pi)=-p(theta) for all theta is said to be Möbius periodic.

A surface given by the form z=F(x,y).

A polynomial x^n+a_(n-1)x^(n-1)+...+a_1x+a_0 in which the coefficient of the highest order term is 1.

A general concept in category theory involving the globalization of local morphisms.

If {f_n} is a sequence of measurable functions, with 0<=f_n<=f_(n+1) for every n, then intlim_(n->infty)f_ndmu=lim_(n->infty)intf_ndmu.

Always increasing; never remaining constant or decreasing. Also called strictly increasing.

A sequence {a_n} such that either (1) a_(i+1)>=a_i for every i>=1, or (2) a_(i+1)<=a_i for every i>=1.