nLab
cube

The nn-cube

Idea

The nn-dimensional cube, or simply nn-cube, is a generalisation of the ordinary cube (or 33-cube) to arbitrary dimensions. It comes in may guises.

As a cubical set

The standard cubical nn-cube is the cubical set represented (as a presheaf) by the object [n][n] in the cube category.

As a topological space

The standard topological nn-cube is the space [0,1] n[0,1]^n, where [0,1][0,1] is the unit interval. The collection of topological cubes forms a topological cocubical set?.

Revised on December 4, 2009 00:39:50 by Toby Bartels (173.60.119.197)