Homotopy equivalence which is suitable for studying Khalimsky nD spaces

In the study of the classification of Khalimsky topological spaces with digital connectivity, the paper develops the notion of k-homotopy equivalence and investigates its various properties. In relation to the discrete geometric transformation, since Khalimsky continuity of maps between Khalimsky spaces has some limitations (see Remark 3.1), the paper uses another continuity instead so that a k-homotopy equivalence is established and it can be suitable for studying Khalimsky topological spaces with digital connectivity. By using the k-homotopy equivalence, we can classify Khalimsky topological spaces with digital connectivity.