Publication detail

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

Original Title

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

Czech Title

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

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.

Czech 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.

BibTex


@article{BUT96346,
  author="Josef {Šlapal}",
  title="A Jordan curve theorem with respect to a pretopology on Z^2",
  annote="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.",
  address="Taylor&Francis",
  chapter="96346",
  institution="Taylor&Francis",
  number="8",
  volume="90",
  year="2013",
  month="august",
  pages="1618--1628",
  publisher="Taylor&Francis",
  type="journal article - other"
}