Abstract
We introduce a new family S of surfaces in the discrete space Z 3 for the usual (26, 6)-adjacency that strictly contains the family of simplicity 26-surfaces and other objects considered as surfaces in the literature. Actually, S characterizes the strongly 6-separating objects of a family S U of digital surfaces defined by means of continuous analogues. The family S U consists of all objects whose continuous analogue is a surface in some homogeneous (26, 6)-connected digital space as defined in the approach to Digital Topology introduced in [R. Ayala, E. Domínguez, A.R. Francés, A. Quintero, Weak Lighting Functions and Strong 26-surfaces. Theoretical Computer Science 283 (2002) 29–66.]. Therefore, S is the largest possible set of surfaces in Z 3 in that setting.
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