COMPLETE LOCAL CHARACTERIZATION OF STRONG 26-SURFACES: CONTINUOUS ANALOGS FOR STRONG 26-SURFACES

In Ref. 6, two similar characterizations of discrete surfaces of ℤ³ 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 26-surfaces coincides with the class of strong 26-surfaces.