Minimal simple closed 18-surfaces and a topological preservation of 3D surfaces

The aim of this paper is to investigate a map which preserves digital topological properties of a digital 3D surface, such as the topological number, digital k-contractibility and so on. Furthermore, the two types of minimal simple closed 18-surfaces MSS18 and MSS18′ are established in Z3 in relation with 18-contractibility, which are shown to be different from each other up to digital 18-homotopy. Moreover, it is proved that MSS18 is the minimal simple closed 18-surface without 18-contractibility and MSS18′ is the minimal Malgouyres’ simple closed 18-surface with 18-contractibility. Finally, we show that a digital (k0,k1)-homeomorphism preserves a simple k0-surface to a simple k1-surface and vice versa.