LAUSR

When digitizing subspaces in the Euclidean subspace in a certain digital topological approach, we are strongly required to preserve topological properties of the given spaces such as connectedness. Thus the present paper studies four kinds of local rules associated with lower limit, upper limit, Khalimsky and Marcus Wyse (for short, L-, U-, K- and M-, respectively) topologies which are used for L-, U-, K- and M-digitizing subspaces of the Euclidean nD space into digital topological spaces. While the L-, U- and K-digitizations are proved to preserve connectedness of objects, the M-digitization has some limitation of having the connectedness preserving (for short, CP-) property. This approach can be substantially used for studying applied topology and computer science.