A digital 3D Jordan-Brouwer separation theorem

Šlapal, Josef

doi:10.2478/auom-2024-0034

Abstract

We introduce a connectedness in the digital space ℤ³ 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 ℤ³. 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 $\frac{π}{4}$ {\pi \over 4} .

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A digital 3D Jordan-Brouwer separation theorem

Abstract

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