A digital 3D Jordan-Brouwer separation theorem

Abstract We introduce a connectedness in the digital space ℤ 3 induced by a quaternary relation. Using this connectedness, we prove a digital 3D Jordan-Brouwer separation theorem for boundary surfaces of the digital polyhedra that may be face-to-face tiled with certain digital tetrahedra in ℤ 3 . An advantage of the digital Jordan surfaces obtained over those given by the Khalimsky topology is that the former may bend at the acute dihedral angle <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mfrac> <m:mi>π</m:mi> <m:mn>4</m:mn> </m:mfrac> </m:mrow> </m:math> {\pi \over 4} .