Publication detail

A Jordan curve theorem with respect to a pretopology on Z^2

ŠLAPAL, J.

Czech title

A Jordan curve theorem with respect to a pretopology on Z^2

English title

A Jordan curve theorem with respect to a pretopology on Z^2

Type

Peer-reviewed article not indexed in WoS or Scopus

Language

cs

Original abstract

We study a pretopology on $\mathbb Z^2$ having the property that the Khalimsky topology is one of its quotient pretopologies. Using this fact, we prove an analogue of the Jordan curve theorem for this pretopology thus showing that such a pretopology provides a large variety of digital Jordan curves. Some consequences of this result are discussed, too.

English abstract

We study a pretopology on $\mathbb Z^2$ having the property that the Khalimsky topology is one of its quotient pretopologies. Using this fact, we prove an analogue of the Jordan curve theorem for this pretopology thus showing that such a pretopology provides a large variety of digital Jordan curves. Some consequences of this result are discussed, too.

Keywords in Czech

quasi-discrete pretopology, quotient pretopology, connectedness graph, digital plane, Jordan curve

Keywords in English

quasi-discrete pretopology, quotient pretopology, connectedness graph, digital plane, Jordan curve

Released

2013-08-01

Publisher

Taylor&Francis

Location

England

ISSN

0020-7160

Journal

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS

Volume

90

Number

8

Pages from–to

1618–1628

Pages count

11

BIBTEX


@article{BUT96346,
  author="Josef {Šlapal}",
  title="A Jordan curve theorem with respect to a pretopology on Z^2",
  journal="INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS",
  year="2013",
  volume="90",
  number="8",
  pages="1618--1628",
  issn="0020-7160"
}