Publication Details
A 3D digital Jordan-Brouwer separation theorem
n-ary relation, connectedness, digital space, digital surface, Jordan-Brouwer separation theorem
We introduce and discuss a concept of connectedness induced by an n-ary relation (n>1 an integer). In particular, for every integer n>1, we define an n-ary relation R on the digital line Z and equip the digital space with the n-ary relation S obtained as a special product of three copies of R. For n=2, the connectedness induced by S coincides with the connectedness given by the Khalimsky topology on the 3D digital space and we show that, for every integer n>2, it allows for a digital analog of the Jordan-Brouwer separation theorem for three-dimensional spaces. An advantage of the connectedness induced by S over that given by the Khalimsky topology is shown, too.
@article{BUT168535,
author="Josef {Šlapal}",
title="A 3D digital Jordan-Brouwer separation theorem",
journal="COMPUTATIONAL & APPLIED MATHEMATICS",
year="2020",
volume="39",
number="11",
pages="1--10",
doi="10.1007/s40314-020-01249-w",
issn="1807-0302",
url="https://link.springer.com/content/pdf/10.1007%2Fs40314-020-01249-w.pdf"
}