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

Český název

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

Typ

článek v časopise - ostatní, Jost

Jazyk

cs

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.

Český 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

Rok RIV

2013

Vydáno

01.08.2013

Taylor&Francis

Místo

England

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",
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.",