Detail publikace

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

ŠLAPAL, J.

Originální název

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

Anglický název

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

Typ

článek v časopise - ostatní, Jost

Jazyk

čeština

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova

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

Klíčová slova v angličtině

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

Autoři

ŠLAPAL, J.

Rok RIV

2013

Vydáno

1. 8. 2013

Nakladatel

Taylor&Francis

Místo

England

ISSN

0020-7160

Periodikum

International Journal of Computer Mathematics

Ročník

90

Číslo

8

Stát

Spojené království Velké Británie a Severního Irska

Strany od

1618

Strany do

1628

Strany počet

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"
}