Lattice (group)
SUBGROUP OF A REAL VECTOR SPACE
Lattice point; Cocompact lattice; Lattice groups; Point lattice; Affine lattice; Lattice model (mathematics); Lattice points; Covolume; Primitive element (lattice)
In geometry and group theory, a lattice in the real coordinate space \mathbb{R}^n is an infinite set of points in this space with the properties that coordinatewise addition or subtraction of two points in the lattice produces another lattice point, that the lattice points are all separated by some minimum distance, and that every point in the space is within some maximum distance of a lattice point. Closure under addition and subtraction means that a lattice must be a subgroup of the additive group of the points in the space, and the requirements of minimum and maximum distance can be summarized by saying that a lattice is a Delone set.