Publication detail

A Jordan curve theorem in the digital plane

ŠLAPAL, J.

Original Title

A Jordan curve theorem in the digital plane

English Title

A Jordan curve theorem in the digital plane

Type

journal article - other

Language

Czech

Original Abstract

We study a certain Alexandroff topology on $\mathbb Z^2$ and some of its quotient topologies including the Khalimsky one. By proving an analogue of the Jordan curve theorem for this topology we show that it provides a large variety of digital Jordan curves. Some consequences of this result are discussed, too.

English abstract

We study a certain Alexandroff topology on $\mathbb Z^2$ and some of its quotient topologies including the Khalimsky one. By proving an analogue of the Jordan curve theorem for this topology we show that it provides a large variety of digital Jordan curves. Some consequences of this result are discussed, too.

Keywords

Digital plane, connectedness graph, Khalimsky space, Jordan curve, Alexandroff topology

Key words in English

Digital plane, connectedness graph, Khalimsky space, Jordan curve, Alexandroff topology

Authors

ŠLAPAL, J.

RIV year

2011

Released

1. 3. 2011

ISBN

0302-9743

Periodical

Lecture Notes in Computer Science

Year of study

6636

Number

1

State

Federal Republic of Germany

Pages from

120

Pages to

131

Pages count

12

BibTex

@article{BUT50522,
  author="Josef {Šlapal}",
  title="A Jordan curve theorem in the digital plane",
  journal="Lecture Notes in Computer Science",
  year="2011",
  volume="6636",
  number="1",
  pages="120--131",
  issn="0302-9743"
}