What is k-cell (mathematics)?

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