A digital 3D Jordan-Brouwer separation theorem
Josef Šlapal · Analele Universităţii "Ovidius" Constanţa. Seria Matematică · 2024
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 π 4 {\pi \over 4} .