  This paper proposes a new cubical space model for the representation of
continuous objects and surfaces in the n-dimensional Euclidean space by
discrete sets of points. The cubical space model concerns the process of
converting a continuous object in its digital counterpart, which is a graph,
enabling us to apply notions and operations used in digital imaging to cubical
spaces. We formulate a definition of a simple n-cube and prove that deleting or
attaching a simple n-cube does not change the homotopy type of a cubical space.
Relying on these results, we design a procedure, which preserves basic
topological properties of an n-dimensional object, for constructing compressed
cubical and digital models.
