Grid cell topology
The grid cell topology is studied in digital topology as part of the theoretical basis for algorithms in computer image analysis or computer graphics.
The elements of the n-dimensional grid cell topology are all n-dimensional grid cubes and their k-dimensional faces ; between these a partial order A ≤ B is defined if A is a subset of B ≤ dim). The grid cell topology is the Alexandrov topology with respect to this partial order.
Alexandrov and Hopf first introduced the grid cell topology, for the two-dimensional case, within an exercise in their text Topologie I.
A recursive method to obtain n-dimensional grid cells and an intuitive definition for
grid cell manifolds can be found in Chen, 2004. It is related to digital manifolds.
