AN EXTENDED DIGITAL ($k_{0},\;k_{1}$)-CONTINUITY

In [8], Rosenfeld's digital ($k_0,\;k_1$)-continuity was introduced and another was also established in terms of the preservation of ${k_i}-connectedness,\;i\;{\in}\;\{0,\;1\}$ [2, 3]. In this paper a new version of digital ($k_0,\;k_1$)-continuity for images in $Z^n$ is referred, which is proved to be an extended version of the formers [2, 3, 8]. The current digital ($k_0,\;k_1$)-continuity is derived from the notion of n kinds of digital neighborhoods with some radius without any difficulties on the dimension and adjacency of an image in $Z^n$. The aim of this paper is to compare among Rosenfeld's digital continuity, the current digital continuity and Boxer's digital ($k_0,\;k_1$)-continuity.