Journal of the
Korean Mathematical Society JKMS

In this paper several continuities and homeomorphisms in computer topology are studied and their applications are investigated in relation to the classification of subspaces of Khalimsky $n$-dimensional space $({\mathbb Z^n}, T^n)$. Precisely, the notions of K-$(k_0, k_1)$-,$(k_0, k_1)$-,KD-$(k_0, k_1)$-continuities, and Khalimsky continuity as well as those of K-$(k_0, k_1)$-, $(k_0, k_1)$-, KD-$(k_0, k_1)$-homeomorphisms, and Khalimsky homeomorphism are studied and further, their applications are investigated.

Keywords: computer topology, Khalimsky continuity, K-$(k_0, k_1)$-continuity, KD-$(k_0, k_1)$-continuity, $(k_0, k_1)$-continuity, digital $(k_0, k_1)$-continuity, K-$(k_0, k_1)$-homeo-morphism, KD-$(k_0, k_1)$-homeomorphism, $(k_0, k_1)$-homeomorphism, Khalimsky l

MSC numbers: 54A10, 54C05, 54C08, 54F65