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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26210%2F13%3APU101371" target="_blank" >RIV/00216305:26210/13:PU101371 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
čeština
Original language name
A Jordan curve theorem with respect to a pretopology on Z^2
Original language description
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 name
A Jordan curve theorem with respect to a pretopology on Z^2
Czech description
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.

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/ED1.1.00%2F02.0070" target="_blank" >ED1.1.00/02.0070: IT4Innovations Centre of Excellence</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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