Complete local characterization of strong 26-surfaces: Continuous analogs for strong 26-surfaces
In Ref. 6, two similar characterizations of discrete surfaces of Z(3) are proposed which are called strong 18-surfaces and strong 26-surfaces. The proposed characterizations consist in some natural global properties of surfaces. In this paper, we first give local necessary conditions for an object to be a strong 26-surface. An object satisfying these local properties is called a near strong 26-surface. Then we construct continuous analogs for near strong 26-surfaces and, using the continuous Jordan Theorem, we prove that the necessary local conditions previously introduced in fact give a complete local characterization of strong 26-surfaces: the class of near strong as-surfaces coincides with the class of strong 26-surfaces.
surfaces digital topology jordan property homotopy