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{FITPUB12321,
author = "Josef \v{S}lapal",
title = "A 3D digital Jordan-Brouwer separation theorem",
pages = "1--10",
journal = "Computational and Applied Mathematics",
volume = 39,
number = 11,
year = 2020,
ISSN = "1807-0302",
doi = "10.1007/s40314-020-01249-w",
language = "english",
url = "https://www.fit.vut.cz/research/publication/12321"
}