1. n. each of a set of independent and mutually perpendicular, or orthogonal, directions in which a Euclidean space may be measured.
2. also called Hamel dimension. the minimal number of mutually independent vectors that generate the given space, that is, in terms of linear combinations of which every element of the space can be canonically expressed; the cardinality of the basis of the space.
3. in particular, the number of coordinates required to locate a point in a space; for example, the space of ordinary experience is three-dimensional, and a flat surface is two-dimensional.
4. various topological measures of size determined by covering properties of the space in question. See also Hausdorff dimension, topological dimension.