Publication detail

A 3D digital Jordan-Brouwer separation theorem

ŠLAPAL, J.

Original Title

A 3D digital Jordan-Brouwer separation theorem

Type

journal article in Web of Science

Language

English

Original Abstract

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.

Keywords

n-ary relation, connectedness, digital space, digital surface, Jordan-Brouwer separation theorem

Authors

ŠLAPAL, J.

Released

17. 7. 2020

ISBN

1807-0302

Periodical

COMPUTATIONAL & APPLIED MATHEMATICS

Year of study

39

Number

11

State

Federative Republic of Brazil

Pages from

1

Pages to

10

Pages count

10

URL

https://link.springer.com/content/pdf/10.1007%2Fs40314-020-01249-w.pdf

BibTex

@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"
}