denseness

Denseness is the quality of being dense—either heavily packed with material or elements, or, in mathematics, of a subset that comes arbitrarily close to every point in a space. The term is used in physics, geography, and pure mathematics, often with different precise meanings.

Physical density refers to mass per unit volume, typically denoted rho. It determines buoyancy, inertia, and how substances interact. Substances may also be described by other densities, such as number density (particles per unit volume) or charge density (electric charge per unit volume).

In mathematics, a subset A of a topological space X is dense if every nonempty open set of X intersects A. Equivalently, the closure of A equals X. The rationals are dense in the real numbers, and the irrationals are also dense in the reals.

Other uses include population density, the number of people per unit area; and packing density, the fraction of space occupied by objects in a packing (for spheres, the densest possible arrangements approach about 74.05% in three dimensions).

Denseness thus describes how thoroughly a space is filled, whether by matter, by points of a set, or by people, and it has precise definitions that vary across disciplines.