Result Details
A Jordan curve theorem with respect to a pretopology on Z^2
ŠLAPAL, J. A Jordan curve theorem with respect to a pretopology on Z^2. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2013, roč. 90, č. 8, s. 1618-1628. ISSN: 0020-7160.
Type
journal article
Language
Czech
Authors
Šlapal Josef, prof. RNDr., CSc., IM (FME)
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
Published
2013
Pages
1618–1628
Journal
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, vol. 90, no. 8, ISSN 0020-7160
Publisher
Taylor&Francis
Place
England
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"
}
Projects
Centrum excelence IT4Innovations, MŠMT, Operační program Výzkum a vývoj pro inovace, ED1.1.00/02.0070, start: 2011-01-01, end: 2015-12-31, completed
Departments