What is "k-cell"

n. (context analysis English) A subset of ''k''-dimensional Euclidean space which is obtained by taking the Cartesian product of ''k'' intervals (closed, open, or half-closed) which are subsets of the coordinate axes of the ambient Euclidean space.

A k-cell is a higher-dimensional version of a rectangle or rectangular solid. It is the Cartesian product of k closed intervals on the real line. This essentially means that is a k-dimensional rectangular solid, with each of its edges being equal to one of the closed intervals used in the definition. The k intervals need not be identical. For example, a 2-cell is a rectangle in such that the sides of the rectangles are parallel to the coordinate axes.