Publication detail

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

ŠLAPAL, J.

Original 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

journal article - other

Language

Czech

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

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

Key words in English

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

Authors

ŠLAPAL, J.

RIV year

2013

Released

1. 8. 2013

Publisher

Taylor&Francis

Location

England

ISBN

0020-7160

Periodical

International Journal of Computer Mathematics

Year of study

90

Number

8

State

United Kingdom of Great Britain and Northern Ireland

Pages from

1618

Pages to

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"
}